couple of thoughts...
Teeth: if it feels as if he is locking his jaw on the 'bad' side rather than his neck it could be teeth. If the mouth stays soft however, you're probably ok.
I'm inclined to not be too quick to say OMG it must be pain if you say he doesn't behave like this in the field... it might just be a mixture of stiffness and just plain not wanting to because it is hard (stiffness) and he's never had to do it before. You can run your hand down his spine and see if he flinches, if not still get the chiro out (especially as you aren't paying!) but also persevere with him under saddle.
Few things to try...
You can bring your inside leg a little further forward to help 'cue' that inside shoulder as you go down the long side. Also try using a stick with a gentle tap on that shoulder to get it to move away from you back onto the rail.
Lots of shoulder in is helpful as is turn on the forehand and turn about the forehand. Leg yield can be good as well in both directions but watch he doesn't just lead with the dodgy shoulder and fall in/out (depending on which rein you are on).
As soon as he starts to fight you and set against you, I would imediately turn him onto a 20m or 15m circle... then ask him to go straight again. You have to be quick to feel his balance shift against you and catch him before he 'locks'.
Try a bit of lunging to see if he can bend without a rider on board.

They've put a man on the moon, but they still can't design a package for likits that you can open in less than 1/2hour