For me since I have a hydraulic press I would use it so the seat is push back in place squarely and not rock into place. You probably can do it with a large c-clamp just want to put even pressure so it goes into straight which what I mean by squarely just you doing with bearings as to not enlarge to the mounting hole.
As pet project it may work fine for personal use but if it was for a paying customer it would be a new head. Your rep as a good repairman is on the line and failure are remembered more than successful work.