the other cases jaynes considers in his "exhaustive case split" are only a tiny, minuscule, arbitrary set of the things that P(AB|C) might depend on.

That's a good point. I suspect that the oversight is due to the fact that the truth value of a conjunction of propositions depends only on the truth values of the constituent propositions, and not on any other structure they might have. I conjecture that the desideratum that propositions with the same truth value have the same plausibility could be used to demonstrate that P(AB|C) is not a function of any additional structure of the propositions, but Jaynes does not highlight the issue or perform any such demonstration.