Some initial thoughts:
1) It's historical evidence such as the above regarding some of the ECFs, employed by credobaptists and lending weight to their assertion, that Scriptural baptism is only adult or believer baptism. This would seem obvious.
2) The historical record is problematic for the Roman Catholic. They claim a direct doctrinal line from the apostles, and an unbroken tradition/practice as the one true church since Pentecost. If in the 3rd and 4th century the RCC as the only true church taught infant baptism and that baptism regenerates and infuses righteousness (as RCs explicitly have since Trent) then this historical record is problematic. Especially when one considers that Gregory's father was a bishop before Gregory was even born and that the others mentioned were raised by Christian parents.
3) On its face this would also seem problematic for the Reformed. He must answer the credobaptist claim and evidence. And that evidence would seem to undermine the Reformed teaching and practice of infant baptism visa-vis God's covenant with his people, baptism being the sign and seal of entrance to the church for children of believers as well as the blessings of the covenant of grace (WCF 28).
I think the Roman Catholics have the more difficult defense to make. Reformed have never attributed regeneration and justification directly to the act of baptism. It isn't hard to imagine that a weakening of the the covenantal understanding of baptism had occurred over a couple centuries after the apostles while at the same time the understanding that salvation received through faith in the gospel generally held firm. Thus Augustine and others were catechized in the the teachings of the gospel with a view to a profession of faith while the practice of baptism for infants receded, at least as practiced in some parts of the church. Without the covenantal understanding of baptism, the church is left with a weak rationale for infant baptism.
Though an understanding of regeneration/grace-infused baptism is found in the ECFs, yet at least as shown by these examples, it wasn't the universal practice of the church to baptize infants for that or any other purpose. The ECFs mentioned above (Augustine, et al) weren't baptized until as adults they came to faith. Rome proudly owns the ECFs as corroborating evidence of their claim to Christ's only visible church. This, it would seem, presents a challenge to Rome's claim of one continuous, infallible church regarding doctrine and practice since the apostles. Its claim to be "The One True Infallible Church" is based on its interpretation of Scripture and its so-called unbroken apostolic tradition/practice. The church's practice of baptism is clearly at variance with that claim in the 3rd and 4th century.
I think the Reformed have an easier case to make. Reformed admit the church, at times, does err and has erred. Yet it remains the Lord's church. Since the Reformation of 16th century there has been a reformed catholic church, one always reforming according to the Word of God. In fact that is the story of the Church from the time of the apostles. To flip around the old 7UP commercial line, "Always has, always will..." Biblical faith and practice have at different times been under assault within the church and thus the church has found itself in need of necessary reform/correction. That's the back story to many of the epistles in Scripture and the front story to the justification controversy addressed in the Galatians' letter. So, it shouldn't be considered an anomaly that the covenantal doctrine and practice of infant baptism weakened in the two centuries following the apostles (or even here and there during their own time). The Reformed church rest upon the doctrines of Scripture alone. If practice/tradition deviate at times, that doesn't undermine the doctrine of Scripture or the legitimacy of the church. What it does is to necessitate a more faithful contending for the faith by the church - 'the faith once delivered' - in its teaching and practice. In other words... the church in this age always has been and always is to be the Church Militant.