> You write that the frequentist doesn't answer the question, but it does. It answers: P(H') = (H/H+T)^H'

The question was asking for P(H' | H, T), not P(H').

> You also write that the frequentist solution fails to give an error estimate, yet you don't show that the Bayesian solution does give one.

Because there is no error? In the proof I assume P(p) is known and then after that every step follows from a law of probability. There is no error to be accounted for in the procedure. The only caveat is that we need to know P(p) to be able to perform the procedure, which is a caveat that I point out at least 3 times in the page.