Is there a reasonable way of applying probability to analogue inference problems?

Your examples, certainly show a grasp of the problem. The solution is first sketched in Chapter 4.6 of Jaynes

Is, in effect, the selection of the underlying model the real challenge of rational decision making, not the inference rules?

Definitely. Jaynes finishes deriving the inference rules in Chapter 2 and illustrates how to use them in Chapter 3. The remainder of the book deals with "the real challenge". In particular Chapters 6, 7, 12, 19, and especially 20. In effect, you use Bayesian inference and/or Wald decision theory to choose between underlying models pretty much as you might have used them to choose between simple hypotheses. But there are subtleties, ... to put things mildly. But then classical statistics has its subtleties too.