How would you deal with this?

So does he do that on the lunge as well? Seems very much like someone has accidentally taught him that.

Needs to go right back to basics, forget the canter issue he needs to re-learn where he should be carrying himself in walk first. Slowly, very slowly build him up over many sessions and if then working correctly the canter problem should sort itself.

I would suspect that he doesn't canter around the field like that, so with a rider on board some real work needs to be done to get him to relax, that means as soon as his head starts to draw in like that, reins should be completely dropped & rider needs to completely relax. Relaxed horse = the only way it will learn.
 
IMO, unless he moves with his head there, in the field, there is an issue about being ridden. Probably the horse is in pain, or at least uncomfortable.
I can't really see the bit in the photo but if it is a gag as others have said, get rid of it, take the martingale off.
If that rider was 'schooling' him, I wouldn't ask her to do it again. She was encouraging him to carry his head like that with the very short rein. She should have been encouraging him to carry himself. Her wrists are bent, which also won't be helping and she looks to be 'perched' on the saddle, rather than sitting deep, to push him forwards from behind.
If you suspect a pelvis problem but the vet can't find anything, perhaps it would be worth getting a chiro/physio to have a look at him.
TBH I doubt if you will be able to right the problem in 6 weeks, those muscles have probably taken years to develop like that and will need at least months to recover.
 
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