What do you mean by "known" physics? Putting a black hole in AdS to prevent it from evaporating is "known" physics in that it's just semi-classical gravity (GR + QFT) in AdS. There's nothing speculative about this. But it's purely theoretical, we don't have any way of experimentally testing this.
I'm not sure what the question actually is. It seems you've already listed several ways in which you can "suppress" black hole evaporation. Are you just asking for some kind of exhaustive list of such options?
There was already a thread about this question not too long ago: https://www.physicsforums.com/threads/conservation-of-energy-in-quantum-gravity.1061153/
"Conservation laws" can mean many different things in gravity. The most conservative and well-understood of these, asymptotic boundary...
q-deformed groups are probably important in some respects for understanding quantum gravity, though I don't know enough about the string theory aspect in particular. But there has recently been some interest in q-deformations in the context of double scaled SYK (which is a proposed boundary dual...
As mentioned, the holographic principle is a conjectured duality between QG and QFT. So it applies to canonically quantized quantum gravity, which is the closest thing to a discrete spacetime. But it's just a conjecture, so it doesn't mean much. The most explicit version of the duality applies...
Not sure if you eventually managed to figure it out but your error is you're overloading indices when taking the variations. Generally speaking, it's better to give separate indices for the field you're taking variations with respect to, compared to the indices in the quantity you're computing...
Not to bring up an older thread, but this is an interesting topic. Most of the conceptual subtleties around conservation of energy in quantum gravity are already contained in classical GR. If you have a spacetime with an asymptotic null/timelike boundary, then energy can be defined at infinity...
Are you specifically interested in black holes that don't evaporate, or black holes that don't emit any Hawking radiation? If it's the former then you can just put the black hole in AdS. If it's a large black hole (i.e. above the typical AdS length scale) then it won't evaporate because of the...
The holographic principle applies to smooth spacetimes. It's a conjectured duality between quantum gravity and quantum field theory. You can expand both sides of the duality in G_N and to leading order you have a correspondence between low-energy semi-classical gravity (with smooth spacetimes)...