If your horse is too reactive to a whip, there's another little trick I know that will deter his attention from the pattern he's making onto something else. If he is broke enough, ride with a halter under your bridle, (or if you have a mecate that's even better) and loop the lead rope through the belt loop in your pants. The rope should go through on the right side through the nearest loop or whatever is most comfortable.
Then, at the walk, just desensitize him a bit but picking up the tail end of the rope and tossing it from one shoulder to the next, gently. If he responds by moving forward, away from it, praise him by letting the rope go or by keeping it still. If you feel he's okay with it, go up into your other gaits and the second you start to feel any balking or hesitation, throw the rope from right to left. If he ignores it, you can let the end lightly thwap him in the shoulder. The rhythm of the rope should not be fast and erratic unless he starts to stop, then you quicken the tempo of tossing the rope. The second he thinks about forward, praise him and start over.
What this simply does it breaks the pattern you guys seem to have gotten stuck in. It's a gentle, non-confrontational way of saying "No, you keep on going." Without your aids having to scream it which usually makes it worse.
While you are swinging the rope you can make some noise, but perhaps time the cluck when the rope goes to the left then to the right.
Pretty soon after you catch him before it happens he'll start to think more of just keeping on going than always planning his next brake check.
Good luck, be safe, and let me know if you have any questions!!