If they're only similarly rational rather than perfectly rational, they'll probably both be biased toward their own estimates. It also depends on common knowledge assumptions. As far as I know two people can be perfectly rational, and both can think the other is irrational, or think the other is rational but thinks they're irrational and therefore won't update, and therefore not get to an equilibrium. So I would disagree with your statement that:

if you and your interlocutor can predict your direction of disagreement, at least one of you is forming needlessly inaccurate estimates

In general, the insights needed to answer the questions at the end of the post go beyond what one can learn from the ultra-simple "everyone can see the same evidence" example at the start of the post, I think.