that makes it sound as if there is some kind of physical stiffness there. Is he unable to bend left at all gaits? can he bend around to the left if you offer him a carrot? Investigate the physical limits of his bending left. And work on him doing this more and more. If you know how to disengage a horse's hind quarters, you might start working on this at the walk, doing it fairly slow and easy at first. The stepping across and under with his inside , back leg is part of what will help loosen his hind end. A looser hind end makes it easeir for the hrose to flex at the poll, and vice versa. So, work on getting him to flex his jaw to the left, so that his head is just twirling on the end of his neck.
And you are working in a snaffle, right? using both hands,?