Thanks for writing this up! I've been wanting to write something on the Ap distribution since April, but hadn't gotten around to it. I look forward to your forthcoming posts.

I find [the Ap distribution] highly intuitive, but it seems to have had almost no influence or application in practice.

There aren't many citations of Jaynes on the Ap distribution, but model uncertainty gets discussed a lot, and is modeling the same kind of thing in a Bayesian way.

On the subject of applied rationality being a lot more than probability estimates, see also When Not to Use Probabilities, Explicit and tacit rationality, and... well, The Sequences.

On the Ap distribution and model uncertainty more generally, see also Model Stability in Intervention Assessment, Model Combination and Adjustment, Why We Can't Take Expected Value Estimates Literally, and The Optimizer's Curse and How to Beat It.