According to Reformed Theology, how can one justify infant baptism?

Yes!

I grew up very firmly in the credobaptist camp, and was taught my whole life that paedobaptism was based in ignorance of Scripture at best and a deliberate disregard for clear teachings of Scripture at worst. But as an adult, having studied the matter for myself without the blinders of my own tradition, the evidence seems to me to at the very least leave room for the concept of paedobaptism. I still can't get behind sprinkling, which is my one remaining barrier to infant baptism.

A sincere look at Scripture has made it very hard to brush aside the references to households and families being baptized. It is hard to believe that the Philippian jailer's family, and even more so Lydia's household (since she was likely wealthy and had servants and their families as well as her own in her household) was comprised only of adults - and even harder to believe that the detail-oriented Luke would have mentioned that whole households were baptised without clarifying that that did not include any infants, when it would be a natural assumption that they would. It is also hard to brush aside, both Scripturally and historically, the fact that there is no evidence that I could find (please let me know if you have found some!) to even remotely indicate that the early church questioned infant baptism - and I don't for a second believe that Jewish parents whose children were previously marked as members of the Covenant did not regularly raise the question of why their children suddenly could not receive the mark of the Covenant when they began to follow Christ. It would look to them as if this new Covenant were excluding their children for no reason. Surely the Apostles would have had to explain credobaptism to Jewish parents often enough that there would be some record of this being an issue.

"Reformed" in this context is perhaps ambiguous. There are Protestants (e.g. Lutherans) that believe in infant baptism (pedobaptism), and there are Protestants (e.g. Baptists) that reject the practice in favor of credobaptism or "Believer's Baptism".

Which one is justified depends on just what you believe Baptism is:

• Credobaptism view baptism as a confession, insisting accordingly that one must be of a rational age in order to be baptized. Acts 8:37 is perhaps a key verse used to argue this point... and does not appear in early manuscripts. Although [credo]baptism is not required for salvation, its nature as an act that we do may strike pedobaptists as a form of works righteousness. (Although they also argue strongly that baptism is not necessary.)
• Pedobaptism views baptism as entirely sacramental. While it does also serve as an outward sign of Christianity, it is God working in us (as in Holy Communion) to effect Grace. As such, there is simply no reason why an infant should not be baptized. The question isn't so much "why" as "why not"? Ironically, credobaptists may feel this is a form of works righteousness. (So, both sides think the other turns baptism into a form of works righteousness!) Pedobaptists may consider baptism necessary, citing e.g. John 3:5.

As I wrote in my answer to Was Martin Luther wrong about baptizing infants?, the debate is not actually about whether or not to baptize infants, but rather it is over monergism versus synergism, particularly in relation to what baptism represents. Pedobaptism is obviously wrong to someone in the synergism camp, while someone in the monergism camp obviously rejects credobaptism and sees no reason to not baptize infants, and many reasons to do so.

During my 40+ years as a Christian (which was marked at the start by full water immersion, as a believing adult) I came to learn much about those who practice paedobaptism, and why they do that. One book written by a Reformed theologian had a chapter on Christian Baptism, parts of which might give the answers you seek. At the start, he makes these points, which are worth bearing in mind:

"I don't regard this debate between Baptists and Paedobaptists as a debate about fundamentals... The divergence itself is not one between Christians and non-Christians. It is very much an in-house division, dividing for example, men such as C.H. Spurgeon and John Kennedy, who on all fundamentals were agreed... those of us who adhere to the doctrine of infant baptism are not necessarily sacramentalists. We do not believe that baptism, by itself, mechanically and invariably effects a saving change in children. We certainly do not administer it in the belief that it automatically regenerates." (A Faith To Live By, p210, Donald Macleod, Christian Focus, Mentor)

As twelve pages are taken to go into reasons for paedobaptism, I shall only select bits that have a bearing on those scripture texts cited in the Westminster Confession of Faith. Only six of those texts are addressed, so I shall confine my quotes to parts dealing with them (though not in that order; they will be highlighted in bold.) It also needs to be said that many other texts are used in the book to support paedobaptism. As I am not answering so as to promote one stance or the other, I shall just try to present in a fair manner what this book says, in its own page order, regarding those six texts.

"Who ought to be baptised? ...Those who are believers! That point needs no demonstration. It is plan enough in the New Testament that adults were baptised on profession of faith. But the Reformed Confessions have gone beyond that and said that we should also baptise 'the infants of one or both believing parents'.

The question is, Do believing parents have the right to have their faith in Christ registered in an act of baptism which includes not only themselves but their families?... the traditional argument of Presbyterians on this issue is still valid. That argument revolves around the fact that when God established His covenant with Abraham He stipulated that the sign of the spiritual covenant should be administered to the physical seed...

In fact, the terms of the Abrahamic covenant make it plain that it was understood by Abraham himself in spiritual terms. The core promise was that God would be his God and the God of his seed (Genesis 17:4ff.) Circumcision was the sign of that promise. This is how Abraham himself understood it; it made him look for a 'city with foundations, whose architect and builder is God' (Heb.11:10).

This is confirmed when we read in Galatians 3:14 that we ourselves as Christians are the beneficiaries of this very same Abrahamic covenant. We are the ones who have experienced the real fruition of its terms and promises. 'Christ,' says St. Paul, 'redeemed us from the curse of the law by becoming a curse for us' (Galatians 3:13). Why? 'That the blessing given to Abraham might come to the Gentiles through Christ Jesus.' And what was that blessing? 'That by faith we might receive the promise of the Spirit.'

The Abrahamic covenant was undeniably spiritual. It was God's irrevocable commitment to Abraham and to his seed. It was the promise of an eternal city of God. It was the promise of redemption from the curse of sin. It was the promise of the Spirit. And when the apostles saw the New Testament inheritance unfolding before their eyes they said, 'This is what God promised Abraham!' Indeed, when Jesus said, 'Go and make disciples of all nations' (Matthew 28:19), he was echoing God's promise to Abraham, 'Through your offspring all nations on earth will be blessed' (Genesis 22:18). The church is sent precisely to bring to all nations the blessing God promised them in Abraham. Yet although it was so clearly a spiritual covenant, the sign was to be administered to the physical seed... on all those born within the family of Israel. That is why not only Jacob but also Esau was circumcised. It is not the elect who receive the sign. It is not the born-again who receive the sign. It is the physical seed... Esau stands there reminding us that not all the physical seed are elect or born again or saved...

It is a remarkable thing that when Christ came He did not institute a new church, but simply grafted the Gentiles on to the old Abrahamic stock. We are the new Israel. We are the Israel of God. We are the seed of Abraham. We are the wild branches grafted into the original olive tree (Romans 11:17ff.) It is a magnificent symbol! God did not plant a separate New Testament church or a separate Gentile church. That is why, when the gospel came to the Samaritans they were not brought to perfection until the apostles came from Jerusalem, and then, in fellowship with the church in Jerusalem, they received baptism in the Spirit (Acts 8 : 14-17).

If, then, it is the same covenant and the same church it seems reasonable to assume that the comforting provision that God made - that when a man comes to faith he may embrace his children with himself under the sign of the covenant - would remain in place. This is precisely what we find... The passages commonly adduced as arguments for infant baptism (e.g. Matthew 19:14, Mark 10:14, Luke 18:16, 1 Corinthians 7:14) merely confirm this. The children of believers continue to have the same special relationship to the covenant as their Old Testament counterparts had; and, consequently, the same right to the covenant sign.

Why do I baptise children? ...It is because God gave me an ordinance: Put the sign of the spiritual covenant on the physical seed." (Ibid. pp 215 - 219)

Now, the entire chapter in this book needs to be read, to do justice to the argument for baptising infants. I have confined myself to your question, and to some of the texts you ask about. I have my own questions about only male children being circumcised, yet male and females can be water-baptised; indeed, I feel a question coming on!

However, this may go some way to showing a Reformed minister's explanation, a man who stoutly agrees with the Westminster Confession of Faith, and who uses some of those texts in his chapter on the subject. I make no judgment here on whether that Westminster Confession is faithful to the scriptures it cites. I simply present a few examples of how they are applied.