I have Arabians. The “up and down” canter is their go-to if there is even a hint of tension in their backs. While I no longer do the hunters, this is still something I deal with often.
The key, I have found, is that these horses are not actually going forward, no matter how “fast” they feel. It sounds incredibly counterintuitive, but you absolutely have to put your leg on and RIDE FORWARD when they get like this. My old 15 hand Half Arab (75% Arabian, 12.5% TB, 12.5% QH) gelding could do the double add when he felt “fast” and would nearly leave a stride out of the lines at 2’6” when he felt slow and relaxed.
Going forward on a horse that feels tense and quick is incredibly hard to do as a rider, but it really is the only way to fix this problem.