Several things occur to me as I read this thread.
1. There is evidence, both historical and from the Fathers, that infant baptism was practiced from the earliest days.
2. There is Scriptural evidence, at least inferred ("households" etc.) and nowhere is baptism of infants prohibited.
3. For the Church to have gotten such a basic practice wrong (i.e. infant baptism) would mean that she was already apostate in the lifetime of disciples of the Apostles.
4. "Age of reason" for baptism is un-Scriptural, and indeed even people who espouse this concept cannot define it or put a limit on it. David has said that he does not know how young someone can be - so why not infants?
So-called "believer's baptism" has always seemed to me to limit God's grace to people who are able to cognitively have a particular kind of religious experience. What happens to everyone else?
Superb summation. May I add one consideration? Regarding the conversion of the entire household, the Scriptures have many citations:
The promise of the angel to the gentile man in Acts 11:13-14: "13 He told us how he had seen an angel appear in his house and say, ‘Send to pa for Simon who is called Peter. 14 He will bring you a message through which you and all your household will be saved.’ "
Lydia and her household in Acts 16:14-15: "14 One of those listening was a woman from the city of Thyatira named Lydia, a dealer in purple cloth. She was a worshiper of God. The Lord opened her heart to respond to Paul’s message. 15 When she and the members of her household were baptized, she invited us to her home. “If you consider me a believer in the Lord,” she said, “come and stay at my house.” And she persuaded us."
The jailer and his household in Acts 16:29-34: "29 The jailer called for lights, rushed in and fell trembling before Paul and Silas. 30 He then brought them out and asked, “Sirs, what must I do to be saved?” 31 They replied, “Believe in the Lord Jesus, and you will be saved—you and your household.” 32 Then they spoke the word of the Lord to him and to all the others in his house. 33 At that hour of the night the jailer took them and washed their wounds; then immediately he and all his household were baptized. 34 The jailer brought them into his house and set a meal before them; he was filled with joy because he had come to believe in God—he and his whole household."
Stephanas and his household in 1 Corinthians 16: "16 (Yes, I also baptized the household of Stephanas; beyond that, I don’t remember if I baptized anyone else.)"
It seems to me that we can look at this from the perspective of the household, rather than any individual member of the household. I think that those household members, who did not have the cognitive functions that seem to be required amongst Baptists--like infants, mentally or intellectually impaired folks, were baptized as part of the group, with the expectation that the group would be responsible for their spiritual growth and welfare. Indeed, I have heard many an Orthodox priest who instructs the parents of an infant to be diligent in bringing them up in the Church.