I’d suggest that since you agree with some parts but disagree with others, you assign probability a lot less than 90% to the whole hypothesis. So you should think I’m irrationally overconfident in the whole lot, and upvote please!
If you want some detail, I start from the “Great Filter” argument (see http://hanson.gmu.edu/greatfilter.html). I find it very hard to believe that there is a super-strong future filter ahead of us (such that we have < 1 in a million or < 1 in a billion chance of passing it and then expanding into space). But a relatively weak filter implies that rather few civilizations can have got to our stage of development—there can’t have been millions or billions of them, or some would have got past the filter and expanded, and we would not expect to see the world as we do in fact see it. The argument to the universe being finite (and not too big) then follows from there being a limited number of civilizations. SIA and MWI must also be wrong, because they each imply a very large or infinite number of civilizations.
No, in that large universe model we’d expect to be part of one of the expanded, intergalactic civilisations, and not part of a small, still-at-home civilisation. So, as I stated “we would not expect to see the world as we do in fact see it”. Clearly we could still be part of a small civilisation (nothing logically impossible about being in a tiny minority), or we could be in some sort of zoo or ancestor simulation within a big civilisation. But that’s not what we’d expect to see. You might want to see Ken Olum’s paper for more on this: http://arxiv.org/abs/gr-qc/0303070
Incidentally, Olum considers several different ways out of the conflict between expectation and observation: the finite universe is option F (page 5) and that option seems to me to be a lot more plausible than any of the alternatives he sketches. But if you disagree, please tell me which option you think more likely.