I deal with this issue on my husbands horse we recently acquired. A few years ago when he worked for a rodeo company "Zorro" was one of the horses in his string for roping bulls and picking up bucking horses. Back then he was light and responsive. Since then and now many people have used that horse, especially for team roping. Which my biggest complaint about some team ropers (This doesn't apply to all ropers of course!) they only lope their horses on the left lead therefor making a very unbalanced horse.
So I have been dealing with the same thing. I am spending a lot of time re-teaching him how to set up for a lead departure. I do a lot of circles with his haunches in. I make sure I can move his shoulders where I want and move his ribs and of course his hind end. When I am setting up for a left lead departure I collect him, drive him over the bit, use my right leg to push his haunches to the left(but not too much as to lose his forward motion) use my left leg at cinch to move his rib cage over to the right, the rib cage has to be moved in order for him to reach up with that hind inside leg. And also I bring his nose slightly into the circle and twist my lower arm as if I was opening a door to pick up his inside shoulder, if the shoulder is dropped he will not pick up the correct lead. When he's ready I will smooch at him to ask for the lope. But I might just ask for proper body position and as soon as I get it from him I release to reinforce that is what I am asking for. This also keeps from anticipating loping off. I see people, and I catch myself, looking at the shoulder while asking for the lead departure rather than feeling it. When you look at the shoulder you automatically lean that way and your not sitting balanced.
I really feel for you, this can be a very aggravating problem. Especially knowing that he is perfectly capable of doing it correctly.
Best of Luck!