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Alex,
The inability of combining QM and GR is a scale related issue and has nothing to do with instantaneous interactions.
QFT (Quantum Field Theory) is a relativistic QM theory.
In the development of QFT the main issues encountered by theorists was that by combining QM and SR (not GR) produced a couple of very strange calculations.
Firstly since QM is a theory based on probabilities, the probability P of a particle being in a particular state is in the range 0<= P<=1.
In QFT however probabilities could have negative values which is of course an absurdity.
Secondly in QFT particles could exist in negative energy levels which is difficult to interpret in QM.
Unfortunately this where a knowledge of mathematics comes into play on how theorists overcame these hurdles by incorporating concepts such as second quantization where a field could be quantized like the characteristics of particles describing energy, angular momentum etc.
Instantaneous travel in QFT is meaningless. It's like trying to explain the double slit experiment in terms of a photon or particle being at both slits simultaneously due to instantaneous travel rather than the Heisenberg uncertainty principle at work, or the photon or particle wavefunction collapsing when an observer makes a measurement. A graviton should it exist will operate on the same principle.
Regards
Steven
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