Congrats on recognizing a serious problem and having the guts to realistically ask if your horse is cut out to do this.
A lot of people never get that far.
That said, I would not give up because he sounds so good otherwise. If he were a pig in other respects, it would actually be simpler, no!
You have two problems, bucking and pulling. The first is pretty serious and it has got to be stopped pronto.
As I do not know where you hunt, and what your hunt is like, it is a little more difficult to address the issue but some things to consider doing:
Say good bye to first field for a while, and go back to second flight, no jumping or if any, very small stuff, and when you feel that buck coming, (you sound like you know what you are doing), nail him before he gets it out. Whatever it takes - you probably know him well enough to know what would work best - definitely different strokes for different horses- but he has got CLEARLY UNDERSTAND that if he bucks, if he even threatens to buck, he will be punished far more severely than the fun/release the buck provides him.
You need to establish a clear and consistent correlation: Bucking = big hurt.
Remove him from the situations where he can get a big buck in and unseat you, put him in a situation where you can control him if he bucks, and then in that more-controlled-and-safer-for-you-environment, deal with the problem THERE where you WILL WIN every time.
Do not let him even begin to get his head down, (you know what comes next!), no galloping or even trotting off down hills, just do not expose him to any situation where you might lose control; in short, ride very defensivley and attuned for that next buck, and nip it in the bud.
It may take a while, maybe even a season, and you will probably need to be on guard for a long time, like if he has the summer off and comes up next fall, he will probably try it again, but it should not be as bad hopefully; that is, if you can solve it this season.
And if you cannot stop it, then there is also the option of employing a pro.
As to the bit, I do not know the mouth piece you are using, but I have found elevators to be highly overrated. Also, do not know how your horse is built and how he is pulling, which does make a difference.
I would do some schooling in the ring and cross country, half halts, asking him to speed up and slow down while galloping/trotting, coming to full halts…all things to get him focusing on your cues. And I would try to use a mild bit.
Then out hunting, try a hard double twisted wire or stronger, a thin knife edge or a single hard twist (ouch). You might need to tie his mouth shut too.
If that does not work, maybe a double or single hard twist gag, they are very effective.
From there, there is a western bit I have seen that is simple but elegant and I would consider it if I must. It is a gag + mouth piece + noseband; works on the poll/mouth/nose, so you are coming at him from every angle you can.
They are on ebay for $30ish, rope noseband with long shanked twisted wire mouthpiece and I think they would easily go on an english bridle. I have seen people with good hands using them on horses that went very well - again, it is like your car, would you drive it with weak brakes? You don’t drive with your foot on the brakes all the time, but when you need them, they had better be working!
I would school him first cross-country with friends and re-create the hunt field, i.e., gallop on a bit and when he begins to pull, growl at him and slow him down, use soft pull, then a pulley rein, jerk him on one side - anything to get him focusing on you and not the horse in front - and hopefully, you will not have to get him to sit on his haunches!
There was a super good article in Covertside maybe 12-15 mos ago, a gentleman in Aiken described how he rehabbed a horrible puller, but I do not recall the method.
Am very interested in hearing other opinions on this matter as it is a common problem.