> letting them pick their own prior multiplies that kind of thing many times over.

I'm a big fan of sensitivity analysis in this context. Don't just pick one prior and call it a day, but show the effect of having liberal vs conservative priors, and discuss that in light of the domain knowledge. That gives the next researcher a much better foundation than a single prior, or a p-value, ever could.

Unfortunately, if it was a non-trivial paper to begin with, it now just turned into a whole book.