If anyone knows of a really good summary for somebody who's actually studied physics on why MWI is so great (and sadly, Eliezer's posts here and on overcomingbias don't do it for me) I would greatly appreciate the pointer.

You say Eliezer's posts didn't do it for you, but how much of it did you read? In particular, the point about parsimony favoring MWI is explained in "Decoherence is Simple". As for the mechanism of world divergence, I think the answer is that "worlds" are not an ontologically basic element of the theory. Rather, the theory is about complex amplitude in configuration space, and then from our perspective embedded within the physics, the evolution of the wavefunction seems like "worlds" "splitting."