I should also note that I'm explicitly asking for rigorous arguments

Many worlds is an interpretation of quantum mechanics. QM stays exactly the same; mathematics, evidence and everything. Whether an interpretation is plausible really just depends on what is aesthetic and what makes sense to you. I explained why some other physicists find Many Worlds reasonable. It's always going to be this nebulous opinion-based "support" because it's not a matter of empirical fact -- unless it ever turned out there is some way the worlds interact.

In my understanding, what you have presented is an argument for why MWI is interesting (is has strong aesthetic appeal) and why it's worth looking into seriously (it doesn't seem to have spontaneous breaking of symmetry).

You've made a distinction between MWI being aesthetic and MWI being worth looking into seriously, which makes it sounds like you view that the argument to avoid spontaneous breaking of symmetry is more than just an aesthetic one. Can you pinpoint the physical reason why we like to avoid it? (I was wondering before.)

And then a question for the physical materialists: Why do you feel comfortable discussing multiple worlds; with it being an interpretation rather than an empirical fact? Or do you think there could ever be evidence one way or the other? (I just read Decoherence is Falsifiable and Testable and I believe Eliezer is saying that Many Worlds is a logical deduction of QM, so that having a non-many-world-theory would require additional postulates and evidence.)