[Maédhros]

In other words, perhaps to a certain extent, the Ring became Sauron's hröa after its creation? Not a full and complete hröa, obviously, but perhaps a PART of it, in a way, just as it became imbued with part of his power.

Thus, although the destruction of his body (twice) weakened him greatly, he continued to survive, not only because much of his power remained intact elsewhere, but because it remained in a part of his "body" elsewhere? Thus, when Frodo destroyed the Ring, it not only cost Sauron his power, but also the last portion of his hröa.

I have to disagree with this. If what you say is true, then Sauron would always survive if his Ring did, but that is not the case.
From the Letters of JRRT: 246

Confrontation of Sauron alone, unaided, self to self was not contemplated. One can imagine the scene in which Gandalf, say, was placed in such a position. It would be a delicate balance. On one side the true allegiance of the Ring to Sauron; on the other superior strength because Sauron was not actually in possession, and perhaps also because he was weakened by long corruption and expenditure of will in dominating inferiors. If Gandalf proved the victor, the result would have been for Sauron the same as the destruction of the Ring; for him it would have been destroyed, taken from him for ever. But the Ring and all its works would have endured. It would have been the master in the end.