What is an overview of Christian viewpoints on the eternal destiny of individuals who die never hearing the Gospel?

I believe there are 3 primary viewpoints to the question, "What happens to those who die without ever hearing the gospel?

The Christian views below are not tied to any particular denomination as there may be some people that attend the same church who would disagree within the denomination.

One viewpoint is: God is evil because it seems like He's sending people to hell because they do not have an opportunity to hear and that's not fair. One Christian viewpoint is: God will someway get the gospel to anyone across the planet who calls out to him, maybe due to seeing his revelation through what has been made. Rom 1. One Christian viewpoint is: God commands that we we share the gospel and we must do so in order for people to be saved. "great commission" Another view point is: The bible doesn't explicitly give us the answer to the question, but we do have evidence that God is Not evil and no one is getting an unfair shake.

People who have never heard... This includes David, Abraham, Adam and Eve, their Children, Daniel, Solomon, Isaac and Jacob, Sampson, etc. These people had faith in God without hearing the gospel message that Jesus died and rose again for their sins. Those they lived imperfect lives, the object of their faith was the One True God. God credited their faith as righteousness and the payment for their sins was made by Jesus. (Romans 1-4).

We do have the Romans 10 passage about the hearing and believing but I think we want to know specifically, "how will God judge those who have never heard the Gospel?" I do not think we get a direct answer to that question. We do however get indirect information that should help us draw a conclusion. 1. No one goes to heaven because they deserve it. (If so there's absolutely no need for Jesus, the cross, and His resurrection. 2. Heaven will be full of sinners like me and Abraham, Adam, Paul, who placed their faith in the one true God. 3. We learn that no sin is a secret sin to God as he knows the thoughts and intentions of each man's mind and heart. Matt. 9:24 When He judges, He has all of the information. There's not going to be missing evidence that was not taken into consideration. 1 Cor 4:5, Luke 8:17 4. He is merciful and good, willing that non should perish. 5. He judges based upon revelation. Each is responsible for the information they have been given. The judgement on the Pharisees was worse because the miracles was done in front of their face. Matt. 11:23

While I cannot directly answer the question, I'm confident that God is good and faithful and will judge with righteousness and justice when He acts.

The God of the Bible wants everyone to be saved:

Have I any pleasure at all that the wicked should die? saith the Lord GOD: and not that he should return from his ways, and live?
— Ezekiel 18:23

For this is good and acceptable in the sight of God our Savior, who desires all men to be saved and to come to the knowledge of the truth. For there is one God and one Mediator between God and men, the Man Christ Jesus, who gave Himself a ransom for all, to be testified in due time, — 1Timothy 2:3–6

The Lord is not slack concerning His promise, as some count slackness, but is longsuffering toward us, not willing that any should perish but that all should come to repentance.
— 2Peter 3:9

Only a relatively small number of individuals will be saved during this current age though.. At Christ's return, they will be resurrected (or instantly converted if still alive), born again as immortal spiritual beings:

in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised incorruptible, and we shall be changed. For this corruptible must put on incorruption, and this mortal must put on immortality. — 1Corinthians 15:52–53

During the Millennium, they will work with Christ, turning the Earth into a paradise and teaching God's way of life to all that have survived the Tribulation:

… And they lived and reigned with Christ for a thousand years. But the rest of the dead did not live again until the thousand years were finished. This is the first resurrection. Blessed and holy is he who has part in the first resurrection. Over such the second death has no power, but they shall be priests of God and of Christ, and shall reign with Him a thousand years.
— Revelation 20:4–6

Notice that "the rest of the dead", i.e. those that have not been saved in the first general resurrection, will be resurrected at the end of the Millennium, in a second general resurrection. This will include the vast majority of mankind. This is the time when they will have their chance to be saved and become part of God's harvest.

Despite the evidence before them, a small number of individuals will inevitably still reject God's grace though:

“Assuredly, I say to you, all sins will be forgiven the sons of men, and whatever blasphemies they may utter; but he who blasphemes against the Holy Spirit never has forgiveness, but is subject to eternal condemnation”
— Mark 3:28–29

Those few unrepentant individuals, the chaff left after the wheat has been harvested, will be destroyed:

Then Death and Hades were cast into the lake of fire. This is the second death. And anyone not found written in the Book of Life was cast into the lake of fire.
— Revelation 20:14–15

This "second death" is compassionate euthanasia by a loving God, not the evil vindictive diety currently followed by most denominations, a god that for all eternity wants to torture all that didn't meet his standards, regardless of why they failed, and all for no apparent purpose other than sadistic vengeance.

Ezekiel 18:23 asks, "Have I any pleasure at all that the wicked should die? saith the Lord GOD". If the true God doesn't get pleasure from death, how could he possibly cause people to experience pain for all eternity? This is not what the God of the Bible wants, but what "the god of this age" spoken of in 2 Corinthians 4:4, Satan himself, wants us to believe.

“For behold, the day is coming,
Burning like an oven,
And all the proud, yes, all who do wickedly will be stubble.
And the day which is coming shall burn them up,”
Says the LORD of hosts,
…
You shall trample the wicked,
For they shall be ashes under the soles of your feet
On the day that I do this,”
Says the LORD of hosts.
— Malachi 4:1–3

The major denominations of Christ's body are shown as to what they believe happens to those who never hear the Good News. In general, the sources do portray that this is their belief within that group.

This link provides a nice overview of general positions and definitions about salvation. For example, who believes the unsaved might be saved post death?

Views on the Destiny of the Unevangelized Universalism Inclusivism Postmortem Evangelism Universal Opportunity before Death Restrictivism -source-

Generally, however, the following are denomination specific beliefs.

Catholic

"Outside the Church there is no salvation"

846 How are we to understand this affirmation, often repeated by the Church Fathers?335 Re-formulated positively, it means that all salvation comes from Christ the Head through the Church which is his Body:

Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.336

847 This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church:

Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience - those too may achieve eternal salvation.337 -CCC-

Orthodox

4. Orthodox believe that by His grace God has revealed and preserved “true doctrine” and “true worship” in the Holy Orthodox Church. The Orthodox Church is the true Church.

Does this mean that all now outside the Church will go to hell? No. Bishop Kallistos Ware suggests that “While there is no division between a `visible’ and an ‘invisible’ Church yet there may be members of the Church who are not visibly such, but whose membership is known to God alone. If anyone is saved, he must in some sense be a member of the Church; in what sense we cannot always say” (The Orthodox Church, p. 248, 1993 edition). Christ our God may be working in others in ways unknown to us and even to them, to bring them to salvation. And in due time, perhaps not till after death, they may recognize God and accept Christ and be united to His Body the Church-so that they can be saved. -source-

Anglican

The Church of Ireland, in common with the rest of the Anglican Communion, is faithful to the Bible’s reticence on this subject and does not require from its members any belief not clearly taught in the Bible. Many questions are left open and we can exercise our judgement on them. For example, is there progress after death or is the final state of each individual reached at the moment of death? The Bible does not give a definite answer to these questions either way. A complicating factor is the question of time in eternity. We cannot assume that time continues in the same way after death as it does before. The day of judgement is not a date in human reckoning that can be known. Judgement may be going on all the time, as some verses in St John’s Gospel suggest (e.g. “Now is the judgement of this world; now the ruler of this world will be driven out” John 12:31). -source-

Protestant

As might be expected, Protestant groups are widely varied on certain specific beliefs, while all would agree we are saved by grace through faith in Christ Jesus. As shown in the first link, there would be a variety of teachings.

As such, I hope this provides a clear overview.

As per OP's invitation to post answers which complement answers already offered I would like to address a specific part of Ken Graham's very comprehensive post. There he lists Exclusivism as the traditional Christian position regarding the fate of the unevangelized and further demarks 3 forms of exclusivism. This answer attempts to flesh out, biblically, most of the third option as Ken presented it below (excepting after death tests):

Nonrestrictive (optimistic) exclusivism affirms that while the fate of the unevangelized is not known, Scripture seems to indicate that God may reach out to those who haven’t heard the gospel in some extraordinary way (dreams, after-death tests, etc.).

Biblically, the baseline starting place is that no one is righteous and everyone is without excuse regarding God's existence and what he requires:

For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who by their unrighteousness suppress the truth. For what can be known about God is plain to them, because God has shown it to them. For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. - Romans 1:18-20

Therefore the holiness and justice of God would seem to be satisfied by universal condemnation and there are some who believe this way (i.e. Restrictive or Pessimistic Exclusivists).

However, part of the revelation that everyone has about God right from the beginning is also the promise of grace and mercy. In what theologians refer to as the Protoevangelium is evidenced the very first gospel (good news) presentation made by God Himself:

I will put enmity between you and the woman, and between your offspring and her offspring; he shall bruise your head, and you shall bruise his heel. - Genesis 3:15

Therefore any acceptance of a mercilessly judicial God constitutes a rejection of the God Who Is.

Paul spoke of this God to the philosophers in Athens who carefully covered their bases with a statue to The Unknown God. In his speech he describes a God who sovereignly places each human life in the time and circumstance where they have the best opportunity to seek God and find Him:

The God who made the world and everything in it, being Lord of heaven and earth, does not live in temples made by man, nor is he served by human hands, as though he needed anything, since he himself gives to all mankind life and breath and everything. And he made from one man every nation of mankind to live on all the face of the earth, having determined allotted periods and the boundaries of their dwelling place, that they should seek God, and perhaps feel their way toward him and find him. Yet he is actually not far from each one of us - Acts 17:24-27

And He has said that anyone who seeks Him with their whole heart will find Him:

For I know the plans I have for you, declares the LORD, plans for welfare and not for evil, to give you a future and a hope. Then you will call upon me and come and pray to me, and I will hear you. You will seek me and find me, when you seek me with all your heart. - Jeremiah 29:11-13

This puts the onus not on God, who has made every provision, but on man who must reject what his sinful heart and the voice of the world system tells him and seek after God regardless of the cost to his current worldview. Thus the call to repent (completely change your mind) and cry out to God. Dedication to a particular religion is not the answer although perception of and fellowship with those who have found God is an intended result:

But as it is, God arranged the members in the body, each one of them, as he chose. - 1 Corinthians 12:18

Now you are the body of Christ and individually members of it. - 1 Corinthians 12:27

Abraham is an example of those who have found "favor" with God in exactly the same way as we do today. They clung to the promise of mercy and grace from God regardless of circumstance, personal failure, human logic, and the voice of contemporaries and are thus reckoned by God as righteous:

By faith Abraham, when he was tested, offered up Isaac, and he who had received the promises was in the act of offering up his only son, of whom it was said, “Through Isaac shall your offspring be named.” He considered that God was able even to raise him from the dead, from which, figuratively speaking, he did receive him back. - Genesis 11:17-19

And he believed the LORD, and he counted it to him as righteousness. - Genesis 15:6

The heart of the difference between those before Jesus' ministry and after is history. Jesus came at just the right time in history and effectively actuated that which was promised. Man is currently required to look back in faith as the Gospel is presented as opposed to having to look forward prior to His first advent but those who have not yet heard the gospel cannot look back. This is why the preaching of the gospel must be done with gentleness, respect, and humility always mindful that we do not know where any person is along the path:

And the Lord's servant must not be quarrelsome but kind to everyone, able to teach, patiently enduring evil, correcting his opponents with gentleness. God may perhaps grant them repentance leading to a knowledge of the truth, and they may come to their senses and escape from the snare of the devil, after being captured by him to do his will. - 2 Timothy 2:24-26

There is now and always has been salvation found in only one Name: Jesus Christ who is the Son of the Living God. Adam, Abraham, David, and countless others all found it without ever having heard the gospel as it is now revealed. If an "isolated jungle man" is saved by the grace and mercy of God having responded to the revelation he has and having sought after Him truly, with all his heart, without having yet heard the fullness of the gospel of Jesus Christ then that is to the glory of God. The responsibility to preach the gospel is not about about getting others to believe exactly what we currently believe but is a presentation of an exceedingly better and fuller revelation toward that end: We are not proclaiming what God will do but that God has done what He has promised. The fullness of God is revealed in Christ Jesus and the presentation of the gospel:

See to it that no one takes you captive by philosophy and empty deceit, according to human tradition, according to the elemental spirits of the world, and not according to Christ. For in him the whole fullness of deity dwells bodily - Colossians 2:8-9

The degree of revelation that a man has received, the degree of acceptance of that revelation, and the degree of earnest desiring of more in the heart of a man is solely the bailiwick of Almighty God. The Calvinists and the Armenians are both pointing to the same essential truths but from opposite sides and they are both lacking in fullness. In order for a man to be saved God must first do something because we are completely lost (He has) and then the man must respond (will we?).

Therefore God may save a man who is responding to the revelation that he has received (that is up to God) but it is infinitely better for that man if he can receive the complete revelation of God that is found in Christ. And so the gospel is to be proclaimed by every believer to every creature as though God Himself were pleading through us:

Therefore, knowing the fear of the Lord, we persuade others. But what we are is known to God, and I hope it is known also to your conscience. We are not commending ourselves to you again but giving you cause to boast about us, so that you may be able to answer those who boast about outward appearance and not about what is in the heart. For if we are beside ourselves, it is for God; if we are in our right mind, it is for you. For the love of Christ controls us, because we have concluded this: that one has died for all, therefore all have died; and he died for all, that those who live might no longer live for themselves but for him who for their sake died and was raised. From now on, therefore, we regard no one according to the flesh. Even though we once regarded Christ according to the flesh, we regard him thus no longer. Therefore, if anyone is in Christ, he is a new creation. The old has passed away; behold, the new has come. All this is from God, who through Christ reconciled us to himself and gave us the ministry of reconciliation; that is, in Christ God was reconciling the world to himself, not counting their trespasses against them, and entrusting to us the message of reconciliation. Therefore, we are ambassadors for Christ, God making his appeal through us. We implore you on behalf of Christ, be reconciled to God. For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God. - 2 Corinthians 5:11-21