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It is easy – if the only problem would be to present a quantum theory of gravity able to recover all the physical predictions of the Einstein equations of GR.
The solution would be quite simple: To break the symmetry of GR adding some term to the Lagrangian which depends on the choice of some preferred background coordinates for space and time. Without the degeneration by symmetry, there would be some technically complex but conceptually unproblematic classical field theory on some fixed background. There would be infinities in the corresponding field theory, but a simple lattice regularization would do the job. These are standard methods used in QFT for other fields too.
If the additional term would be small, and the distance between lattice nodes too, there would be no way to measure effects of these distortions.
But this simple way is a no go. Because it would require a different metaphysical interpretation. In principle, the distortion of relativistic symmetry could be used to identify a preferred frame. From a practical point of view, not a problem. We have, anyway, for all practical purposes, a preferred frame – the CMBR frame. But this is nonetheless anathema, it would violate a Holy Principle of Modern Physics.
But if the Equivalence Principle in its strongest form (SEP) is Holy, then there is no way to quantize it. The fundamental concepts are too different.
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