GR and QM are so well tested experimentally in their domains of validity, i.e. classical and microscopic respectively, that I say that any experiment in those domains that purports a violation will be found to be bad experiments - errors of one sort or the other.
Not only that, but in this particular case: (to one claim - details not relevant)
1) I don’t see how GR is even relevant in this experiment
2) the problem will be in the condensed matter physics part of the experiment.
Of course, that does preclude natural extensions of GR and QM to expanded domains - analog to analytic continuation of a real function of a real variable to a complex function of a complex variable.
e.g.
3) “quantum gravity” attempts of various kinds
4) torsion fields coupled to quantum spins and even orbital angular momentum of Tuv sources?
5) mesoscopic and macroscopic coherent phenomena in pumped open dissipative structures - does Born probability interpretation break down in the manner suggested by Antony Valentini in a series of papers? In this regime is the dynamics fundamentally non-unitary with entanglement signaling (e.g. using distinguishable over-complete non-orthogonal Glaubereigenstates of non-Hermitian observables of relatively sharp wave amplitudes and phases).