I have a similar problem. My horse likes to trot or canter with his nose 6" from the ground. Usually it's to put his head between his legs and buck around the ring. He also like me to hold his head up. He can be heavy in the turns. I have had a hard time finding the right bit. I want to have light hands but he leans so much that it becomes me holding his head and hanging on his mouth. I put my leg on and it works until I give and back goes his head in my hands. Any suggestions? He also likes to go fast to avoid the bit. Trot fast, canter fast, gallop and buck. He doesn't do this with other riders usually.
What type of bit are you using? I find very often bits with just a single joint can hit the horse's pallet (roof of their mouth). Many horses will lean hard into the bit so all the pressure will hit their bars and tongue and not hit their pallet. They'll also often drop their head to the ground so the bit is tilted in a way that it doesn't hit their pallet as easily. They will also often run through the bit as it hurts and stopping doesn't work so they push through it instead.
I would look for something like a french link or lozenge style bit (like the KK ultra). This should help a great deal with his leaning. I typically prefer a more structured ring like a D or full cheek for the added lateral pressure (pushing on the outside of their lips to help push their head correctly). But if you find the horse still leans you might want to look into a loose ring.
Have you had this horse's back and teeth checked? Saddle and Bit fitted?
If he does this only with you something in your communication is missing, are you bouncing too much and hurting his back? Are you using your hands to balance and driving his mouth crazy? You don't need to answer on here, just think about it and decide if there's something you're doing that could be bothering the horse - if he doesn't do it with other people there is a reason. Are you relying too much on the bit for turning?
If you find you're relying too heavily on the bit for turning and slowing start practicing using your seat more. Start by riding the horse doing several different figures in the ring, switch it up constantly so he never knows what you're doing. Figure 8s, big circles, little circles, diagonals, tear drops to reverse directions, cut the center line, do circles in the middle of the ring. The more you change things up - using your entire body to steer more than your hands - the more he's really got to pay attention. Changing gaits the entire time up and down constantly - all this will fine tune your horse's listening skills as he'll always be ready for a cue and listen more closely when you begin to shift your weight and seat for the next cue.