I can see the "hitch" in his right shoulder when he's in his intermediate gait.
I'm not sure the head toss is anything more than the rider having too tight a rein when he asked for the turn.
I would want to know the PPE vet says about the right shoulder or it could even be saddle fit that has caused soreness and maybe he needs a chiropractor.
Orrrr maybe the soreness is down in the hoof but there's a hitch in the right front coming from somewhere. Just because he sounds to be hittin' a lick solid on all fours, doesn't mean the hoof can't have something going on. Horses being prey animals are very stoic about hiding their hurts