I think your answer may be that the horse isn’t suitable for hunting.
However, you’ve gotten some good advice here. I personally ride my horses with a zero tolerance for bucking and that holds from day 1. Any indication of bucking and they get spun. I use the one-rein stop and disengage their hindquarters.
I’m too old to have a horse buck me off in the hunt field and I find it’s easier to never tolerate the behavior.
I do think it’s best if you can head off the behavior – once they start to put their head down or you feel that hump in the back, that’s when you need to let them know that you will not tolerate it.
I’m always cautious about advising people to gallop their horse until it’s tired and then some. I tried that on my TB the first year I had him. He got so geared up that I thought if I could get him tired, I could teach him to listen to me. He taught me that he didn’t really get tired. After galloping him 12 times around a huge field, I was exhausted and he was a snorting dragon. He finally learned that lesson after a four hour hunt, but some of these horses are darned hard to tire out.
Personally, I’d get a trainer on him that can ride the corrections and see if you can eliminate the behavior in the ring first, then out on the trails or at a hunter pace before trying to hunt him.