Teaching a SB to canter can be done! I got my SB as a three yo pacer who didn't pass time trials. Back then, she couldn't canter more than a few strides without getting her legs muddled up and reverting to a trot or pace.
I taught my horse to canter by lunging and free lunging to allow her to sort out her legs without the interference of a rider and by discouraging pacing. Whenever she would try to transition to a canter, she would often start to canter but make a mistake with her legs and end up pacing. Once I was getting a few consistent strides of canter while lunging I moved to riding. When she paced while riding, I tapped her gently but rhythmically with the crop while half halting until she came back to a trot so she learned that pacing was uncomfortable. Once she had settled back to a relaxed trot, I would ask for a canter again until she got it right. Its important not to over do the cantering because they can get overwhelmed and tired and stop trying.
Now, my horse hasn't paced in years! Be patient though - I've seen SBs that have the living daylights thrashed out of them for reverting from pacing to cantering on the track. You have to be gentle when retraining because otherwise they panic thinking that you will do the same thing.
When I bestride him, I soar, I am a hawk: he trots the air; the earth sings when he touches it; the basest horn of his hoof is more musical than the pipe of Hermes. ~William Shakespeare