I think the way you put it, "have a feel" of his mouth, is best. Contact won't create a dull horse if it's meaningful contact.
You kind of have to ride either with your reins long enough that you aren't following his mouth with your hands (you would be hard put to follow it, since you cannot feel his mouth) and if you want to transmit a message through the reins, you pick up the needed rein and if the hrose is really sensitive, just the feel of you picking up the rein, not even any pull on the bit, will get the message across. Of, if he isnt' sensitive, you'd have to pick up a LOT of rein to get to the place where you have enough contact for him to respond. Your horse you say is really sensitive, so he hardly needs any contact.
OR, you have your reins short enough that you are always feeling the horse's mouth, all the time, but just in a nuetral and soft way , and this allow you to follow his mouth (the action of his head bobbing) because you can feel it move up and down. This way, you hardly have to shorten the rein, indeed, you mearly squeeze your hand tighter to make the horse give to that side, becaus he is already connected to both reins.
If you ride somewhere in between that, then as the horse is moving its' head with its' gait, the reins go loose/tight/loose/tight and the hrose gets bopped with each stride.
Does that make sense?