You can't stop this by going after the individuals. That is like stopping a swarm of bees one bee at a time. The root problem remains - to win, you need to make a horse move in a completely false manner. It seems to me you have to ban the use of the equipment used, and require 100% vet checks of EVERY horse, EVERY show. It might require a legal ban on 'big lick', just like we ban cock fights.
The video below was made by a supporter of this form of competition. It turns my stomach to see horses used this way. Beetle-like humans, hunched on the horse while the horse does something freakishly unnatural...it says something very repulsive about human beings.