Well I don't know much about string halt so I don't know exactly how that changes the situation, but assuming like you indicated in the post your horse simply has underdeveloped muscle tone for cantering and lacks practice, I can offer some advice. It is of course normal for a green horse to not naturally understand the concept of leads.
However, horses traveling on the wrong lead, especially when being asked to bend, will not be balancing correctly and will feel uncomfortable. We, as trainers, can use this to our advantage in teaching correct leads. The first question, however, I would have is whether your horse has mastered his leads on the ground yet or not.
If the horse has not worked much cantering on the lunge line, and does not pick up the correct lead lunging, then this is where I would start before teaching leads under saddle. When lunging, especially at the canter and extra-especially because your horse has a health condition(!), it is important that the lunging circle is large enough for him to canter comfortably on the correct lead. The key here is that this circle will not be comfortable should he pick up the incorrect lead.
If you are lucky, and your horse does not automatically pick up the correct lead on the lunge circle, he will perform a flying lead change. If you are slightly less lucky, he will break into a trot, in which case you can keep asking for the canter until he picks it up on the correct lead. In the worst case scenario, you may have to bring him back down to a trot or walk yourself and keep asking, even tightening the circle for the initial transition and widening it once he picks up the correct lead.
Once you have your horse moving out at the correct lead in a nice circle, maintain the canter for long enough to allow the horse to get used to the feel of the correct lead, as well as to build up his muscles. This is especially important when working on his difficult lead, as this will allow him to develop muscle and also be more comfortable moving correctly.
When you get to the point that your horse gets his leads correctly most of the time on the lunge, or if you would rather start off working from the saddle, you can move on to the next step. When you practice picking up the correct lead from the saddle, it helps to ask for the transition on a circle or in a corner, so that the horse is bent correctly. Setting up our horses for success is always important! If he does not pick up the correct lead, do not try to force a flying change in the saddle at first. Instead, immediately bring him back down to a trot (but not so roughly that he feels he is punished for taking the canter cue of course!) and ask again and again until you get that lead. You will get it eventually, I promise. Once you are in the lead, continue to canter for awhile to build up those muscles, just like you would on the lunge line. Work especially on his more difficult lead, as this is what needs the most work! Eventually he will figure it all out, just be patient with him!