Actually, let me put that another way. The only scenarios I've been able to imagine for "moving to another branch of the wave function" seem indistinguishable from a combination of 1) a precise copy of all the particles and fields that compose your body coalescing randomly in that "other universe", and 2) all the particles and fields composing your body in "this universe" spontaneously vanishing.
That's certainly possible (and thus there are presumably branches of the wave function where it happens). But I can't see any mechanism by which you could create a causal connection between those two events (as I said before, decoherence would seem to make doing so impossible, at least on an effective level). And without a causal connection, they might as well be independent events. At that point, either one on its own would be vastly more likely than both together: no time travel necessary.
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That's certainly possible (and thus there are presumably branches of the wave function where it happens). But I can't see any mechanism by which you could create a causal connection between those two events (as I said before, decoherence would seem to make doing so impossible, at least on an effective level). And without a causal connection, they might as well be independent events. At that point, either one on its own would be vastly more likely than both together: no time travel necessary.