If we allow for the many-worlds hypothesis, then the universe is infinitely large

OK, you have a good point. I was not considering each branch to count as an entire new space that we need to add up with every other branch. I guess I'm talking about our current branch, right now. Also, I could easily be wrong but I think there are no branch points that create an infinite number of new branches and so there still may be an insanely vast but finite number of branches.

So no probability assertion about the universe's scope should, rationally speaking, have anything remotely resembling a high threshold of confidence. Said confidence should, in fact, approach zero.

I think that if you take Occam's Razor seriously, then you never have uncertainties that literally are zero. (I don't know what approaching zero would mean in this context).