QM says nothing of the sort. QM simply predicts that the two measurements will correlate when compared at a later time. — noAxioms

I was under the impression that Bell's inequalities showed that the indeterminacy of the particles properties was a real aspect of nature and that the measurement of one effects the measurement of the other. These measurements can take place within an interval of time in which light is not fast enough to travel between them in order to relay the information.

What you appear to be saying is that we cannot speak of one measurement 'causing' the other measurement to be a certain way. At least that is what I infer from what you've said. But isn't it implicative in what you said that some real event takes place by which the measurement of one entangled particle affects the measurement of the other at some point, or across some very minute interval, of time? This is an assumption that you seem to be avoiding and yet would logically be expected.

After doing a bit of research there's this experiment wherein retrocausation appears to occur and is why, I suspect, there's a reluctance to use causation in relation with entanglement - the delayed choice quantum eraser experiment. This happens without any input from relativity. It's interesting because in some way the state of the particle's superposition is itself in a state of superposition with non-superposition of the particle. The problem might be resolved if you think of the particle hitting the screen as the measurement that decides the path of the other entangled photon?

And to add to what noAxioms said, you seem to be confusing eternalism, which the theory of Relativity does not assert, with relativity of simultaneity, which it does. But for your question, relativity of simultaneity is what you actually need, so no harm done — SophistiCat

Sorry, I meant to say no universally present moment.