You need someone to teach you how to use the outside rein. While there are two reins and held at the same length, they have very different functions. This horse sounds like he has been well schooled, albeit using controversal techniques. If you start "wiggling the reins" to get him to soften, you'll have him BTV in no time. Try this exercise. First make sure your reins are dead even. Be sure that, with your elbow hanging at your sides, you have a straight like from elbow to bit. Again, not tight contact, but enough that if he stretches his neck, he can find your hands. At the walk, ride squares. Use your entire body (two hands, two legs, seat), not just hands, to turn him at each corner. Each time you get to a corner, feel how your horse steps into the outside rein. Each time you turn, your horse should step under his center of gravity more and you should feel him reach for that outside rein. If you can take a few dressage lessons to give you some more input about the importance of the inside leg/ outside rein connection, all the better.
You just have to see your distance...you don't have to like it.