I don't see how they're going to overcome their differences. It's not just feelings be real doctrinal issues where I don't think the Eastern churches would ever accept even the old position of Rome as a first among equals.

What I can see instead is in a century or two something like what's going on with the Anglican church and Catholicism where there's a slow cohabitation going on as the congregations stop caring and start flittering between the two churches.