I agree, more training. Teach him to disengage his hind quarters and execute a 1-rein halt. I would use a full cheek french link, so you have more turning power. Also teach him to round his neck and back, and give to bit pressure.
If you are determined to ride him on the trail or out of the arena before you solve this issue, I would use a low port kimberwicke, but ONLY for work outside the arena. You need to teach him to pay attention to his rider and give to the bit willingly, which you won't be able to accomplish with a bigger bit. You'll only give him the oppotunity to learn how to evade and run off with more bit
I would also look at his diet. Diet plays a big role in horse behavior. Make sure he's on no grain, or a small amount of low starch pellets or a ration balancer. If he's on alfalfa hay, switch him to a "calmer" hay like Timothy or Bermuda. Make sure he gets at least 6 hours of turnout a day, preferably 24/7. If he's on lush early spring pasture, consider a grazing muzzle.