Francis Beckwith wrote:
"After all, if Catholic soteriology were merely a Roman invention, its presence in the Eastern Churches in one form of another would be unlikely. And yet it is there, in spades: seven sacraments, infused grace, etc. So, in a sense,the universality of this soteriology shifts the burden to those who claim it is 'unbiblical.'"
Why do you have to refer to the soteriology "in one form or another"? Because there are many differences, in addition to the similarities.
And why should we think that the soteriology in question was "universal"? Roman Catholicism and the Eastern churches you seem to have in mind aren't the only groups that existed at the time or that have claimed some sort of pre-Reformation lineage. Anglicans, Waldensians, and others have made such claims as well. Even in Roman Catholic circles, there was a wide diversity of soteriological beliefs at the time of the Reformation and in earlier generations. See here. Somebody like Thomas Bilney could believe in the papacy and transubstantiation, yet be sympathetic to a Protestant view of justification. For some examples of soteriological diversity in patristic times, see Augustine's comments in The City Of God 21:17-27. See, also, here.
Was belief in seven sacraments, to take one of Francis Beckwith's examples, universal in apostolic times? No. In patristic times? No. In the Middle Ages? No. The Eastern Orthodox bishop Timothy Ware writes:
"Only in the seventeenth century, when Latin influence was at its height, did this list [of seven sacraments] become fixed and definite. Before that date Orthodox writers vary considerably as to the number of sacraments: John of Damascus speaks of two; Dionysius the Areopagite of six; Joasaph, Metropolitan of Ephesus (fifteenth century), of ten; and those Byzantine theologians who in fact speak of seven sacraments differ as to the items which they include in their list. Even today the number seven has no particular dogmatic significance for Orthodox theology, but is used primarily as a convenience in teaching." (The Orthodox Church [New York, New York: Penguin Books, 1997], p. 275)
If the concept of Roman Catholicism's seven sacraments becomes popular, not universal, so late in history and under such dubious circumstances, what significance does that popularity have?
What about "infused grace"? Many groups could be said to believe in some form of infused grace, involving a combination between grace and justification through works. The concept of justification through works is popular, and not just in professing Christian circles. Any group of professing Christians is likely going to include grace in its view of justification, even if it contradicts the Biblical definition of justification by grace by means of the inclusion of works. A professing Christian, whether a Mormon, a Roman Catholic, or whoever, is going to claim to believe in justification by grace. The fact that the groups Francis Beckwith mentions have believed in some form of "infused grace" isn't of much significance. Such beliefs were popular prior to the Reformation, but some professing Christians believed in concepts such as justification through faith alone and the preservation of the saints (eternal security) in pre-Reformation times as well. See the articles linked above for some examples. Again, why should we think that the Roman Catholic view was "universal"?