I think it could get a lot more complicated than that. I edited my post to include a link to the DGA's website and I think they may be very interested in this.
Sure, if Trank decides he doesn't want to ruffle any feathers or burn any bridges, he could choose to walk quietly away . . . but that doesn't seem to be the way this is going down.
If they, hypothetically, release the film without his name, he can claim that he was director throughout principle photography and they didn't give him any credit, that's a violation of his rights as director.
On the other hand, if they release it with his name on it while he was barred from post production, they have also violated his rights as director.
And even if his legal case is weak, the simple act of filing legal papers and then waiting for a trial date could delay the film until the rights run out.
And Trank's biggest concern is getting another job . . . but he theoretically has another job . . . with Disney. They may have already dropped him in which case he's screwed anyway, but if they haven't dropped him, would they warn him: "You better not file legal action against Fox if you want to keep your job."? Not only might the DGA have something to say about that, but I can't imagine Disney taking such a stand in this particular case.