OK, the "surreals" contain the transfinite ordinals, hence they contain the infinite cardinals as well. So, surreals can indeed model universes of strictly infinite size i.e. not just non-standard finite size.

I think the SIA problem of weighting towards the "largest possible" models still applies though. Suppose we have identified two models of an infinite universe; one says there are aleph0 galaxies; the other says there are aleph1 galaxies. Under SIA, the aleph1 model gets all the probability weight (or decision weight).

If we have a range of models with infinities of different cardinalities, and no largest cardinal (as in Zermelo Fraenkel set theory) then the SIA probability function becomes wild, and in a certain sense vanishes completely. (Given any cardinal X, models of size X or smaller have zero probability.)