I think that Solomonoff Induction already gets us to the conclusion we want, with the problem that it is relative to a language. So one way to put your point would be this: "There is no fact of the matter about which language is 'right,' what really exists is an infinite unordered jumble of universes. In order to think about the jumble, much less describe values over it, we must fix a language with which to describe it. Why not pick a language that favors a certain pleasing kind of simplicity? And hey, if we do this, then thanks to SI it all adds up to normality!"

Retreating into the impregnable swamp of infinity may save you here, but it is a dubious move in general. Compare to someone who thinks that they will win the lottery, because they believe in a Big World and thus there are infinitely many copies/futures that will win the lottery.

Edit: Thank you, by the way, for this conversation and discussion. I'm very interested in this topic and I like the way you've been thinking about it. I hope we can continue to make progress!