Sometimes the "backward" training works well. Going from harsher bit, one with more leverage, to softer. If you use operant conditioning, a very basic training technique, you will have success.
I've found that if I can pair leg and seat cues to the absolute of a harsher bit, I can eliminate the need for leverage all together. The bars of a horse's mouth are more forgiving than most of us think. You don't even need sensitive bars in order to have a handy, responsive horse.
My kids are great examples. They grew up riding lots of spoiled/ruined horses and one summer each took on two BLM feral horses. They got bored with the normal cues and trained their mounts to respond with all sorts of silly cues. Honestly, hand sewn carrots strung on fishing poles was one of them. Carrot out in front = go at whatever speed their scrawny legs indicated. Carrot taken away = stop. It worked! Craziness.
Then there was the fly swatter silliness. The three of them trained some to respond to a fly swatter placed in specific spots. To shake things up: fly swatter on the shoulder was "go," fly swatter on the hip was "stop."
Sure, they then eliminated the weird cues. We needed to sell these horses. But they did prove that basic psychology worked no matter what.
So, do what you want, or are comfortable with, most likely with repetition your horse will eventually figure it out. If it doesn't, try something different, or come back here and rant. Whatever.