You have openned Pandora's box, my dear. You will get tons of advice from people telling you that you need to work on your horse's training , rather than turning to a different bit to solve this lack of brakes problem. And, truth is, that's probably the best thing to work on.
As for a bit, you could try a thinner bit, if you want a tiny bit more "bite". Perhaps not a Baucher. Ever heard of or seen a PeeWee bit? It's basically a MUllen mouthed thin bit and it might help.
But mostly , you will want to work on building your horse's sensitivity to the bit in general, and teaching him to come "off" the bit when you ask him to stop. To not only stop, but to rock his body backward and halt with his weight on his back legs, and wait for you to ask him to move on.
Or, you could try something totally different like a hackamore.
But ultimately, it's having the horse respectful of what the bit means and you being as light as you can when you can and as strong as necessary to get him to come off and not get into a stalemate.