I think that the correct way to make sense of all the weird stuff that plagues QM is not by increasing the number of dimensions or state superpositions (ie: Many Worlds interpretation) but going exactly in the opposite way: reducing the number of dimensions, and trying to see things as the massless quanta that perform all our interactions do.

In my opinion, massless quanta show entanglement not because they get connected on another dimension, but precisely because the dimensions that we observe are not present for them. Our spacetime reality is not different than their adimensional reality. What really happens is the same thing, but experienced in two completely different ways.

Also, in order to explain how electrons and other matter particles can show entanglement and interference, we just need to realize that matter particles are just recurrent field patterns or structures, where the disturbances that shape them also propagate at the speed of light.

Matter particles are just resilient combinations of entangled and causal interactions. When the level of complexity grows, the causal interactions are much more evident than the entangled interactions that support them, and we start getting classical physics behaviour.

Lately I have had long comments rejected, so I will try to elaborate this in another comment.