What is far from clear - to me at any rate - is whether super-rational agents can share perfect knowledge of both the first-person and third-person facts and still disagree. This would be like two mirror-touch synaesthetes having a fist fight.

Why not? Actions are a product of priors, perceptions and motives. Sharing perceptions isn't sharing motives - and even with identical motives, agents could still fight - if they were motivated to do so.