Jaynes? Didn't you mean Aumann?

Sorry, my bad.

I think drilling for the reason might help. If you keep asking, innocently, playing a dumb devils advocate ("But what do you mean by X? How does Y justify Z? I don't understand why Q, etc.") and then you can at some point criticise her for believing in strange things that she can't explain to you in simple terms.

Roll up your sleeves and use the 37 ways words can be wrong, is my advice.

Orthogonal idea: Find some way to incite cognitive dissonance with her world view on the basis, perhaps, of object level morality.

On a personal note I happen to almost only interact with Traditional Rationalist or Very Sane For Common Man persons, so I have little practical knowledge of this.