It would not be handwave: there were a lot of reform movements trying to act from within the Church, including by people like Erasmus.
Erasmus was an orthodox Catholic. There's no such actual category as "reform movements" in real life. Different people had different ideas on how to make reforms, but where it comes down to points of doctrine, we would have to look at the specific doctrinal formulae one by one.
The biggest hurdles are the doctrines of transubstanciation and predestination, but other aspects could be accepted by the Catholics: some where accepted at the Vatican II (granted, almost 500 hundred years later, but...).
No offense, but it doesn't seem like you have actually read about this very much. For example, there is the issue of not only transubstantiation, but the remaining six sacraments. None of those are going to go away. Luther rejected five of the seven. Besides that, there's purgatory, vicarious satisfaction, canon law, Petrine supremacy, and the various issues of Christian anthropology which rely on a different underlying metaphysics altogether. Luther, for example, had never read the works of St Thomas Aquinas, whose theology AND philosophy were and still are hugely influential (perhaps more than any other) throughout the Church. Another issue is justification, the sources of ecclesiastical authority, etc. These are almost all defended by Catholic theologians with staunch loyalty. Look at St Thomas More as an example of the sort of loyalty for doctrinal principle that would be very common in the face of a more politically successful Protestantism.
What also seems to be hand waved away, incorrectly, is the Catholic belief on predestination. The consensus view among approved Catholic theologians (that is to say, theologians who are given the license to speak and publish as theologians recognized by the Church, which was especially important during this time period of the early sixteenth century), to this very day, is that there IS predestination, as is taught by Thomas following St Augustine. Of course, this idea of predestination is quite different from Protestant ideas about it, but it's there.
Disciplinary reforms are much easier, of course, but the Catholic theological system and legal corpus as such are pretty complete. One cannot simply posit that one thing would just go away without it affecting the rest of the entire system. It's frankly not even true to say that Vatican II even changed anything below a superficial level.
I would encourage looking into the historical facts on this subject.
It would not be otl's Lutheranism nor Calvinism, but what if (maybe because of reduced temporal papal power) some of the reformers' worries and questions are acceptes by the mainstream Church? This would at the same time ensure maximum extent to "a" reformed Church and minimum extent to "the" reformed Church of otl, which would likely be reduced to a marginal heretical movement.
Sounds like a bloodbath, since there would be widespread schisms and turmoil.
