You know, I am not a trainer, so take my thoughts here with that in mind.
I am having a little trouble visualizing what you are explaining. So,he is going around a circle, let's say to the left, and then he has decided at a certain point that her wants to go right and he lets his haunches drift out to the right?
Is this a correct synopsis?
Your trainer has tried circling him in one spot when he does this. Is she circling with his chosen direction or against it?
It sounds like he would "rather fight than switch". (a very old and lame jingle form the days when cigarettes were advertised on TV) and you mentioned that he is willing to fight much longer than any horse either of you have ever met. I read in Mark Rashid's book that his mentor told him, "horses are almost always willing to fight if you bring them a fight" or something to that effect.
Maybe, just maybe, if he moves his haunches out of the circle, you just go iwth him; the direction he wants to go. You give him nothing to fight against. You just give way and let him choose the direction but you have him keep moving, regardless of where. It might end up looking like a crazy quilt of movement. Eventually, you would add a trot to this strategy. He deflects himslef off the track you have set (at a walk). Ok, if you want to go that way, we will, but we'll trot there.
I have NO idea if this would work. I am just thinking off the top of my head.
Good luck and post a video sometime if possible.