It is sort of like a "seesawing" motion, back and forth using both reins.
You say you do that because he is so sensitive in the mouth and you believe it's softer than pulling. That is NOT true. Not to mention, if your horse was sensitive in the mouth, he would stop if you gave him a tug on the reins.
So to get him to stop, do a million transitions. Walk, halt, back up, walk, halt, trot, halt, walk, trot, walk, halt, walk, etc. Only take a few strides in between each transition. And use your breathing. Start at the walk, take a deep breath in, and on your exhale, gently squeeze with your fingers, tighten your core, and stop moving with your horse's forward motion. If your horse isn't completely oblivious to your presence on his back, he'll hesitate, if not stop altogether. If he just hesitates, try again with a little harder of a squeeze with your fingers. If you two are as in tune as you say you are, it won't take him long to catch on. It's also a good idea to add a back up to almost ever halt you do. And it is perfectly acceptable to ask your horse to go from a trot to a halt, so don't be afraid to ask. Good luck, and PLEASE, stop see-sawing.