Bar's withers are not just steep, they are long. Even nice pads with wither cut-outs don't have a hole big enough to give him complete wither freedom. Peter suggested being sure to create some space between Bar's withers and the pad, too. I've tried that in the past, but not had a lot if luck keeping the space there while I ride. Must try harder.
And it's definitely the withers where we are having issues. I could recreate the twitch simply by touching that bony protrusion after our lesson yesterday. On the plus side, I could also get him to walk it off when it would flare up during the lesson.
He is still getting a visit from Wonder-masseuse Karen tomorrow because I think it will help. It certainly won't hurt, that's for sure.
The saddle we are trying also seems to be working. It's wide enough for him, stays off his shoulders and is high enough to give good wither clearance. It also stays in one place, which us fairly important. My saddle tends to slide back which means it is likely too narrow for Bar.
Glad the puzzle pieces are fitting together. And, yes, glad I was over-reacting too.