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> The only way I can see to escape this madness with MWI seems to be give up on the notion of truly separate branches, and instead treat these “many worlds” as a stream of overlapping world-ish-nesses in which discrete outcomes don’t actually even exist

That's what it is. A measurement is coupling a quantum event to a statistically irreversible process. The total wave function that results has two major lobes. There's no split on measurement. That's why it's appealing: it makes no reference to classical mechanics in the formulation.

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