I don't see your conclusion holding. I am inclined to say: Therefore there are no distributions which that, regardless of how much money you find in envelope A, envelope B still has an equal chance of being twice as much or half as much.

I suppose "numbers selected from all the numbers in the series 2^n" and so forth are ruled out of being distributions based on the "infinities and uncomputable things are just silly" principle? (I am fairly confident that) something on that order of difficulty is going to required to provide the envelopes. A task that is beyond even Omega in the universe as we know it but perhaps not beyond an intelligent agent in the possible universes that represent computational abstractions natively.