I'm gonna weigh in as a long time trainer of English Hunter/Jumpers. I've seen a lot of one-sided horses.
This is what I want you to try. First, use a snaffle so you can direct-rein your horse for training purposes. (Once she's good at picking up the left lead, you can switch her back.)
Going to the left, use direct outside (right) rein, turning her head slightly to the right.
Then - you want to position her with her left shoulder in... like this: (
To get her to do that, use direct pressure at the girth with your outside leg (right leg) to push her left shoulder toward the inside.
Use your inside leg (left leg) positioned behind the girth to keep her rump at the rail... so rump and head toward the rail, and inside shoulder to the inside of the ring.
Do this from a walk, and cue her very firmly into a canter in this position using your outside (right) leg.
By pushing that one shoulder in, you're placing her balance in such a way that to stay balanced, she must pick up the correct lead. It may take a number of tries, but it will work - I promise.