Axioms

Ah, ok, I see. To make meaningful use of the entanglement you'd have to bring the clocks back together (or communicate between them, but that's essentially the same -- there is frame-switching no matter what). But this is exactly the setting of the twin paradox [1] which is a more well-known example of trying to equivocate between events in distinct frames.

[1] https://en.wikipedia.org/wiki/Twin_paradox