Hokey Smoke, Bullwinkle! A reining Paso!
Well, short of suggesting you don't gallop him in open country, let's treat him like a reiner and focus on WHEN you ask him for a stop rather than how. The bunny hop effect usually comes from a horse that is trying to stop on the forehand. And that's a timing issue. He's received the stop cue when his hind feet are still on the ground or just about to make contact with it. That makes it impossible for him to round his back and get his hindquarters underneath himself. So he tries to plant those front feet and can't handle all the impulsion still coming from behind. Thus, he gets vertical with the stop.
Try asking for the stop as the hind feet are coming up and forward. That gives him a chance to get under himself in preparation for a smoother stop. To do that you'll need to initiate the stop cue as the saddle cantle is coming forward to slap your butt. Most riders ask for the stop when the saddle is down low because it feels like a more secure seat. But if the saddle is down low your horse's hind feet are in contact with the ground. And in his immediate attempt to comply the weight and momentum goes down on the front... hard! And he'll go vertical with the momentum to keep from blowing over onto his head or over reaching with the hind feet and hitting his own front legs.
Get thyself and thy reining Paso to an arena, transition from the trot to a canter or gallop and IMMEDIATELY, within a stride or two, ask for a stop... while the saddle is rising to meet you... before he builds up too much impulsion. This is just an exercise for you to practice your timing. When you get it right the bunny hopping should go away or be at a minimum. As your timing for the stop cue gets better you can let him build up a few more strides before asking for the stop. If nothing else, this will also cause the horse to rate his own speed and be a little more collected, anticipating that stop cue at any time.
After you get the stop cue timing worked out, get him shod in sliders and hit the show circuit. I think people will pay money to witness a reining Paso. ~FH