In modern gravitational physics you can treat components of the Einstein or stress-energy tensors as like these energies, e.g. for a family of observers, the apple-breaking kinetic energy is like the pressure components (T^ij, i=j, i!=0 ~ \gamma mv^2) and mostly in T^zz or T^rr or whichever, depending on one's choice of system of coordinates. However, simply by changing frame of reference, at each point where we find the apple/applesauce transition we can shuffle the whole of T^zz into one or more of the other components in G = T (keeping that relation invariant), and it is really stretching things to suggest that a change of coordinates is a process in the sense of the question in your first sentence.
> In general relativity black holes are not actually comprised of matter---they're entirely warping of spacetime
Well, that's not true of stellar collapse black holes; whatever you want to make of the trapping surface / apparent horizon, it encloses matter that existed before that formed. You don't need quantum anything, or even any future infalling, to deal with the fact that there is real matter inside at the time of formation.
The Schwarzschild vacuum solution is matter-free, but then astrophysical black holes of all masses and all origins generally do not truly source the Schwarzschild metric, just a usefully close approximation.
What you can say is that whatever's inside a black hole, eventually it will bald all its "hair" and can be effectively described (by an outside observer) at any point in time in terms of its spatial position (3 components), linear momentum (3 components), angular momentum (3 components), electromagnetic charge (1 component), and mass (1 component), with any other features irrelevant in the Kenneth Wilson sense. That is, eventually it doesn't matter whether it was all neutron degenerate matter or whether there were some other particles inside the horizon when it formed, but there was some matter there: the apparent horizon around V616 Monocerotis didn't just pop up spontaneously far from any matter.
Quantum gravity only matters if you want to make guesses about what state the matter is in within the horizon (assuming you're unhappy about it inevitably being crunched into an infinitesimal point as in classical General Relativity), or about what it looks like when during evaporation the horizon retreats far enough to expose that state. I'll assume you favour keeping unitarity in any solution to the AMPS firewalls problem, and would happily ditch the apparent validity of the EFT outside the horizon. :-)
