When riding at home, do you practice standing still on a slack rein (on the buckle)? If he doesn’t do it at home, it’s hard to expect them to know how to do it out hunting. I’d work on practicing standing with a slack rein. Halt, give him a verbal cue, “stand”, release your contact. If he steps off, collect a rein quickly and have him do a small circle until you get him to halt again. Give him a pat once he has halted, verbal cue, drop the reins again. It will take LOTS of practice, but you can make it happen.
Making corrections with the rein, i.e. yanking on the rein, tend to not work. You just end up in a battle for the reins. Using a touch of the spur, or crop can help correct the behavior, but you must be consistent and respond quickly.
One of my geldings WAS AWFUL about rooting and usually while at a check. It seemed to be a bit of a boredom issue. He was a bit wigged out by crops when I first got him, so I would use my spur each time he started with the rooting. It was never used in anger or harshly, but it wasn’t the result he was looking for. It took a bit of time, but he eventually quit the behavior, and it was a STRONGLY instilled one. He was a beginner lesson horse before I got him. He would root with the smaller riders. When he had a really small rider on, he wore an overcheck so that he couldn’t pull them.
Having a horse that was pretty much foot perfect in every other way out hunting for their first times, I’d take a horse that rooted at a check over some of the other “bad behaviors” I’ve seen and experienced.