But that's an issue of QM, irrespective of the particular interpretation.

No, it isn't. QM is purely causal and relativistic. You can look into the equations and prove that nothing FTL is in there. The closest you get is accounting for the possibility of a vacuum bubble having appeared nearby a particle with exactly its energy, and the antimatter part of it the bubble then cancels with the particle. And that isn't much like FTL.

When you do an EPR experiment, the appearance of FTL communication arises from the assumption that the knowledge you gain about what you'll see if you go check the other branch of the experiment is something happens at the other end of the experiment, instead of locally, with the information propagating to the other end of the experiment as you go to check. The existence of nonlocal states does not imply nonlocal communication.