Your "general frameworks for combining" do exactly the work that logical positivists did by building statements from verifiable constituents using logical connectives....So, even without invoking omnipotent beings to check whether the cake is there, the logical positivist would attribute meaning to that claim in essentially the same way that you do.

I agree that EY's attacking a certain straw-man of positivism, and that EY is ultimately a logical positive with respect to how he showed the meaningfulness of the boltzman cake hypohteses. But, assuming EY submits to a computational complexity prior, his position is distinct, in that there could be two hypothesis, which we fundamentally cannot tell the difference between, e.g., copenhagen, mwi, and yet we have good reason to believe on over the other, even though there will never be any test that justifies belief in one over another (if you think you can test mwi vs. copenhagen, just replace the universe spawns humans with 10^^^^^10 more quanta in it vs. it doesn't, clearly can't test these, not enough quanta in the universe).