So my horse crosses his jaw while working, sometimes sticking his tongue out. It seems like he crosses his jaw, sets it, and just blows through me. He had his teeth done a few weeks ago. I currently use a baucher bit or a 3-ring elevator bit (I know not dressage legal...we use it when we go out riding in the field or jumping).
I was reading an article the other day were a BNT eventing clinician had recommended removing the noseband (and flash, obviously!) because if both are tight the horse can actually set their jaw against the noseband and exacerbate the problem. The riders were so impressed with how much better the horses went that they continued riding without nosebands. I tried it the other day with my TB who is rather prone to rushing and setting against me while jumping and without a noseband it really did feel like she couldn't set against me the same way (and I didn't even have a flash previously). Might be something radical to try - can't hurt to try it once!