What do you think about Relational QM? That's where I'd put most of the single-world, comprehensible-to-this-layman probability. It doesn't seem to require faster-than-light influence on a real particle or any obvious non-locality.

RQM as an alternative to MWI seems to just assert that if we take correlations as fundamental, we find that only one history holds together logically. I do not expect this to hold, because if it did then I'd need a reason not to expect a proof that MWI is impossible. But perhaps if I understood the topic better I would find it unfair to demand such a proof.