I am not familiar with that bit, so no comment there but in my experience and in my opinion draw reins are not going to fix the problem they are only putting a band-aid on it. The way I have fixed this type of problem in the past is do lots of lateral flexion. Start on the ground in a halter teach the horse to give laterally with light pressure, then do it from the ground using a snaffle bit. Horses learn from the release of pressure so as soon as he gives you his nose release. When he gets light on the ground do it from his back, first at a stand still, then ask for a walk and stop him with one rein when he softens release. When he is light at the walk move to a trot then a canter. If he resists bump him off the bit with rein. Make sure to practice on both sides, if he goes to fast at a trot shut him down with one rein you may only get three or four strides then shut him down. Vertical flexion begins with lateral flexion. Your horse has a stiff body something that stronger bits and draw reins will not fix.