Have you tried teaching him to stretch to the bit? When I horse stretches down, he has to un-tense both his back & his neck, and it sounds like he is locking his back & maybe his neck as well. A few years back, the 1st level dressage tests required that the horse, on command, stretch down to the ground, or as low as he could/would go, the lower the better, and come back up again when asked, without resistance or fussing about it. Doing this demonstrated that the horse was relaxed enough through the neck and back to stretch down without changing his speed, rhythm, or stride length. And it demonstrated suppleness and balance in that he could do the above without changing his speed, rhythm or stride length.
You start out at somewhat of a disadvantage, being a smaller person on a very big horse, so if you can teach your horse to do this, you will be able to un-tense him elegantly, and keep him at the end of whatever length of rein you chose to give him. To go down smoothly on command without jerking the reins through your hands, the horse has to be relaxed, and again to come smoothly back up on command without fussing or fighting the bit requires that he stay relaxed through both his neck and back. And, once you have taught him this, you have will have a method of getting him to relax through his back and neck.