Well, there's really no reason for a schoolmaster to be behaving that badly. So, that brings in the question of pain and/or saddlefit. Have you have x-rays taken on any part of the back? Depending on age, he could have arthritis in his back and the vertebrae could be attempting to fuse at one location or another. A rider could trigger pain. I'd personally toss him on MSM. It works on most horses and does an AWESOME job at reducing inflammation caused by arthritis or injury.
How is his muscle development in the back? Is his back smooth, or does it have obvious muscle development? Is his spine higher than the muscle? Does he have atrophy behind his withers? What about at his neck in front of the shoulder? There ought to be a triangular muscle bulge extending from the base of the neck at the shoulder. If he lacks muscle there, that's a sign he hasn't been moving correctly, which can be a sign of pain. Even my fat old pasture mare has kept some of her back/neck muscle simply because she moves properly.
If that all checks out, then look at saddlefit next. You ought to post pictures for us. A lot of people think that adding a bunch of sheepskin fixes back pain. It really doesn't... And even if there's clearance in the front, the saddle might hit the spin further down the back. Post parallel side views of the entire horse standing on level ground from both sides with the saddle in proper position (girthed or ungirthed) with NO saddlepad. (You don't look at english saddle fit while using a saddlepad). Then get an angle where we can see how the flaps fit to his shoulder blade but step back enough that we can see most of the horse to get a reference point. (Both sides). Post one photo of you standing directly behind him, level ground, camera the same height as the channel of the back pads. (When you're looking at it, let us know if you can see daylight shining from the other end).
And make sure we get a photo of the pommel showing wither clearance through the channel.
This will make sure we can rule out saddle fit.
Once we determine it's not pain or saddlefit, we can help you write a work schedule.