Which way around do the harness horses race in the region this horse came from, Gabby? Here they race anticlockwise, i.e. circle-left, i.e. if you were cantering that, it would be on the left lead (unless you were performing a counter canter). My hunch is that your horse raced mostly anticlockwise, and perhaps the trainer wasn't 100 percent dedicated to working the horse both ways in training (many don't). This then results in a "sided" horse.
This also happens to TBs, for similar reasons. My saddle fitter says that she sees a lot of off-track horses, both TB and SB, who have not been worked equally in both directions and whose bodies have deformed because of it. They will be more muscular on one side than the other, and sometimes their spines will have curved sideways. The older the horse is at this point, the longer it will take to correct the problem. What you need to do in that case is to consciously work the horse to build up the opposite side, by spending more time, in your case, working on circle-right etc, and going clockwise around your arena. Uphill-downhill work is also great.
To do this effectively though, you need to spend no less than 1-2h five times a week (building up gradually) working with your horse, and mostly not at a walk. Free-lungeing at the trot and canter, preferably in a sand yard, and say 70% on circle-right, 30% on circle-left until the horse gets more even, is also fantastic, and in some ways better for the horse than ridden work, as it doesn't have to try to deal with a rider while it's so out of kilter. Realistically though, I'd say, divide your time between lungeing and riding. Just work the horse harder when lungeing, at least for the first three to four months. Remember it must work up a gentle sweat in each session (assuming cold weather) and be out of breath. Recreational riding horses don't work nearly as hard as racehorses, and at the usual recreational pace, it may take you a decade to significantly address the problem as opposed to a year or so. (It will take at least a year. Problems that have developed over quite a few years also aren't quick to fix.)
Best wishes!
Some trivia: Many SBs are also worked in harness at the canter on sand tracks, by the way. Trotting or pacing is the most efficient way for them to move on firm, level surfaces (like race tracks), but in deep sand the canter is more efficient. The idea that the canter is "beaten out of" SBs in training is a myth. It's just that some trainers under-utilise the canter in training, and don't do this kind of sand training.