If, to continue on a bit about a theoretical twelve, there were any voluntary giving up of power by the various patriarchs (including the Pope) I would imagine it could be legitimate in the same sense as God is self-limiting that we might have free will. Of course, they wouldn't technically be giving up power, but merely excercise it in unity, as the twelve. We no longer have merely the few issues that caused schism; we now have entire ecumenical councils in the intervening years, and we hold these to be legitimate. So how then, could we hold these to be legitimate but hold them open to some kind of revision, which would almost surely be necessary to get other churches to validate them?
That's what I think the twelve could do. Of course, it would be far easier if everyone would just listen to the Pope, but we can't even get Catholics to do that, now can we? Or this could be downright stupid, but then what's a blog for?