See the problem?

Not really. You keep demonstrating my point as if it supports your argument, so I know we've got a major communication problem.

The form of the reasoning presented originally is valid. That is what I was defending.

And that's what I'm attacking. We are using the same definition of "valid", right? An argument is valid if and only if the conclusion follows from the premises. You're missing the "only if" part.

It wasn't: when a certain form of argument is asserted to be valid, it suffices to demonstrate a single counterexample to falsify the assertion.

Not for probabilistic claims.

Yes, even for probabilistic claims. See Jaynes's policeman's syllogism in Chapter 1 of PT:LOS for an example of a valid probabilistic argument. You can make a bunch of similarly formed probabilistic syllogisms and check them against Bayes' Theorem to see if they're valid. The syllogism you're attempting to defend is

P(D|H) has a low value.
D is true.
Therefore, P(H|D) has a low value.

But this doesn't follow from Bayes' Theorem at all, and the Congress example is an explicit counterexample.

So you can actually form a valid probabilistic inference without looking up the specific p(H)/p(E) ratio applying to this specific situation -- just use your max entropy distribution for those values, which favors the reasoning I was defending.

Once you know the specific H and E involved, you have to use that knowledge; whatever probability distribution you want to postulate over p(H)/p(E) is irrelevant. But even ignoring this, the idea is going to need more development before you put in into a post: Jaynes's argument in the Bertrand problem postulates specific invariances and you've failed to do likewise; and as he discusses, the fact that his invariances are mutually compatible and specify a single distribution instead of a family of distributions is a happy circumstance that may or may not hold in other problems. The same sort of thing happens in maxent derivations (in continuous spaces, anyway): the constraints under which entropy is being maximized may be overspecified (mutually inconsistent) or underspecified (not sufficient to generate a normalizable distribution).