A very thought provoking question. Thanks for tingling my neurons 😂 I think The many universes interpretation doesn't specifically solve for interference, that's a result of quantum superposition, the superposition itself can exist in "many worlds" and the process of the observer entangling with the wave function of the photons will create new branched universes where observers in different branches will experience different outcomes of the superposition. This is my understanding, maybe someone else can improve on it.

Thanks for discussing! My specific issue is, I've heard mwi described as saying there is no wave function collapse - all that happens is you, as an observer, end up in a branch that contains a single outcome from all the superposed possibilities - eg an electron hitting the detector at a certain place after going through alone slit or the other. It is implied that nothing special happens before this, and observation just strips out all the other possibilities ("destroys the worlds"). But the electron at the detector has the properties of a particle not a wave. If so something must have changed and the only thing that makes sense to me involves some sort of "collapse" from waves that can interfere, to particles that are detected. Which seems not to be allowed under mwi. As an aside part of my interest in this is that I feel quantum mechanics may indicate a special role for the observer that puts it outside of the physical world, and can help make sense of many things in our experience that science hasn't been able to inform us on. More on this if you are interested!