Hm. The simplest way around this is to treat the fact that an immeasurable disjoint set B exists as new information to our agent. E.g. if you just tell me to bet on hitting some immeasurable set A, I'll think the possibilities are just (A) or (not A), and in my state of ignorance will bet at 1:1 odds. But if you then tell me there's some disjoint set B, now the possibilities are (A), (B), (neither). Maximum entropy dictates that I only assign a 1/3 probability to hitting A or B. This handles the dutch book correctly.

If you add knowledge about relationships between a jillion more immeasurable sets, it still produces sensible answers. The biggest trouble I can see is that representing the things we know about relationships between immeasurable sets in this way is tedious.