I don’t have knowledge on these topics beyond some YouTube videos, but if you entangled two particles and then transported one to Alpha Centauri, wouldn’t you have a common “now” if you were able to transmit data between them?
I find it's easier to understand if you assume that every entangled particle already "knows" what state it will be at the moment of entanglement. In theory it's called "hidden variables". John Stewart Bell has proven that there's no local hidden variables, but noone said about global variables. For example, in Superdeterminism it's all easy and clear.
PS: Physicists thet reject Superdeterminism only for philosophical reasons, there's no scientific reasons to reject it.