The merger with the state fundamentally changed your sect. As power was consolidated, any sect which disagreed with your interpretation of Scripture, practices, or was unwilling to subjugate themselves to your domination was branded traitors and heretics. The Donatists are a good example.
The Donatists objected to the ease with which those that denied Jesus, helped destroy Scripture, and aided in the persecutions were allowed not only back into the church, but assumed positions of authority. The were also opposed to the union of church and state. I believe they only practiced adult baptism, by immersion and had a congregational form of church government.
If you look at that list I think all of these different sects had these features to a lesser or greater degree. IOW, you can find throughout history, prior to the Reformation, sects of Christianity that refused to submit to the domination of the state religion and sought Scripture as the primary guide. Thus, the idea that the Reformation was the first time that the primacy of Scripture, Sola Scriptura developed is wrong. I think you will find the same is true for all the other Sola's.
Calvin? Luther?
Problem with that view is that all the fundamental doctrines of the Church were fully formed way before Christianity became Rome's state religion, as the patristic evidence shows.
I agree that at times Protestantism resurrects old heresies, donatism especially often. But these heresies were smashed on their merits (donatism was argued against by St. Augustine, the only Church father the Reformers want to hear from). I doubt that you'd find much ideological kinship with any of the old heresies in toto.