Soteriology: How does God save free moral agents?

I would say read the book of John, specifically John 1:1-14, 6:44 onward, 14:6 onward, and Acts 4:12 onward. These scriptures will give you some good beginnings to understanding how man comes to God.

There is an Eastern Orthodox article on the difference on the original patristic difference between Ancestral Sin vs. the later Western Augustinian "Original Sin". That I encourage you to look at it, since it touches on your question. I will quote a bit of it below and give a look to it emphasizing a few lines that deal with your question.

"The Fall could not destroy the image of God; the great gift given to humanity remained intact, but damaged (Romanides, 2002). Origen speaks of the image buried as in a well choked with debris (Clement, 1993). While the work of salvation was accomplished by God through Jesus Christ the removal of the debris that hides the image in us calls for free and voluntary cooperation. St. Paul uses the word synergy, or "co-workers", (I Corinthians 3:9) to describe the cooperation between Divine Grace and human freedom. For the Orthodox Fathers this means asceticism (prayer, fasting, charity and keeping vigil) relating to St. Paul's image of the spiritual athlete (I Corinthians 9:24-27). This is the working out of salvation "with fear and trembling" (Philippians 2:12). Salvation is a process involving faith, freedom and personal effort to fulfill the commandment of Christ to "love the Lord your God with all your heart, soul, mind and strength and your neighbor as yourself" (Matthew 22:37-39)."

https://www.stmaryorthodoxchurch.org/orthodoxy/articles/ancestral_versus_original_sin

"How does God save moral agents?" would be a question that could be answered by Christians who believe the Bible to be the inerrant word of God. But you added the adjective, "free", without qualifying what you mean by "free". You assume that everyone will have the same understanding as you, but that is an unwise assumption.

This site requires the OP to identify a particular group within Christianity to answer. So, if you asked Christians who believe the Bible to be the inerrant word of God to answer, the danger of having your question closed for lack of focus would be avoided. Or, if you wanted to search for the Catholic view on this, you could ask Catholics to answer (or any other group - just name them).

My answer is that of a Christian who believes the Bible to be the inerrant word of God (therefore my answer comes from the Bible). Adam and Eve certainly were free to choose whether to obey God, or to disobey him. They were without sin. But once they sinned by disobeying God, they lost their freedom. They became enslaved to sin, and from there-on-in, they could never break free from captivity to sin. They could still make good, wise choices regarding living as humans, but once sin had corrupted human nature, it spread, and so all humanity is enslaved to sin (Romans 5:12 & 18-21). That is why the question of "free" is questionable. How can enslaved people be called "free"? What good does all the freedoms their captor allows them do, when they still remain captive? Sin is a vicious captor and never lets its captives free. When it comes to choosing spiritual matters, we are all dead in trespasses and sin (Ephesians 2:1). We will always make sinful choices unless God delivers us from our spiritual deadness, so that we come to spiritual newness of life.

This leads to the answer to your question - How does God save - from always making sinful spiritual choices? Isaiah 61 foretells the coming of a Saviour - one who proclaims freedom to the captives, and release from darkness for the prisoners". Jesus applied that prophecy to himself when he began his earthly ministry. Read Matthew 11:5 and Luke 7:22.

Romans chapters 6 & 7 explains this miracle, showing how God enables us to be "set free from sin" - through the gift of God, which is eternal life in Jesus Christ our Lord. Paul could exclaim that "through Christ Jesus the law of the Spirit of life set me free from the law of sin and death" - Romans 8, the whole chapter. Jesus Christ is the "how" for those who put faith in him alone to be set free.

As for your other question, "How does the freedom of choice intersect with saving faith and the work of the Holy Spirit to convict us of sin?" - that requires to be posted as a separate question (and, again, addressed to a particular Christian group). As your question here stands, it is dealing with a vast topic. This site requires focused questions, one at a time. Then progress can be made.

From my answer, you might begin to see merit in dropping the words 'free' and 'freedom' if you do post another question. I respectfully suggest that by looking at the way God saves sinners without the human assumption that we are free (whatever that's supposed to mean), blinkers might drop off, to enable a very different perspective.