You don't want to ask him to do this???
My TWH is not terrifically 'well gaited' - he doesn't have the steepness to his croup, coupled with the angles of his hind leg, and his femur is too short, and his hocks a little too high...to really reach under and go deep. But his regular walk and his canter are lovely. It's all in how they are built.
But then, we knew that