I think you are overestimating the difficulty of the mathematical problem here! To quote JoshuaFox:

(Two impossible things before breakfast … and maybe a few more? Eliezer seems to be rebuilding logic, set theory, ontology, epistemology, axiology, decision theory, and more, mostly from scratch. That's a lot of impossibles.)

But once those problems are solved, we do not need to additionally solve the problem you are highlighting, I think...

'Try to prove to the satisfaction of your opponent that their view leads to too many circumstances we both agree are problems. Avoid question-begging arguments, i.e., ones that assume that your logic is the right one, when that is precisely what is under dispute; seek arguments that both of you can agree are valid, or even arguments that you think are invalid but that you think problematize your opponent's position.'

When it comes down to it, wouldn't this be just like some logic that is the common subset of the two, or perhaps some kind of average (between the probability distributions on observations induced by each logic)? Again, I think this will be handled well enough (handled better, to be precise) by a more powerful logic which can express each of the two narrower logics as a hypothesis about the structure in which the environment is best defined. Then the honest argument you describe will be a result of the honest attempt of the agent to estimate probabilities and find plans of action which yield utility regardless of the status of the unknowns.