If you understand the Everett interpretation, those experiments stop being spooky-action-at-a-distance. Instead they become a prediction about a system at one locality will interact with a system at another locality when they rejoin.
The trade-off is that your picture of reality has to become much weirder.
I'm not a big fan of the Everett interpretation. It seems too contrived. I prefer to think of spooky-action-at-a-distance as the nature of the wavefunction is such that its domain is all particles in the universe (which it is, since splitting it up for single particles is an approximation). Problem solved.
I do not understand what you think is contrived about it. To me the assumption that quantum mechanics does not describe the human brain is much harder to swallow than the Everett interpretation is.
The trade-off is that your picture of reality has to become much weirder.