As far as his 'food driven' issue - give him a bit of a break! He's just learning how to be a 'horse'. His attention span and cooperation will improve as he gets older and more experienced.
I agree however if he starts doing this well before the end of the session and should be listening to you, then you have two possibilities.
1) To counter act the "bulge" shorten the outside rein and cause the horse to bend looking to the outside of the circle then slowly put more inside leg on him to straighten him out (keeping the outside rein as a shortened rein) until he comes into contact with the outside rein and maintain forward gait while doing this. A stop is something I would never do as you want the horse thinking forward...not stopping.
2) Allow the bulge to a point but turn the horse into the center of the ring so he is in a "shoulder in/leg yield" type position. Continue forward movement but apply more inside leg with a stiffer ( meaning ungiving) outside rein. This should put the horse almost into what is called a "volte in motion" but you will not allow a circle but rather a leg yield while still maintaining the larger circle position. So in effect the horse will face the inside of the circle while leg yielding in the direction the motion originally started and still doing the larger circle.