I totally agree with most of the people on here but I thought I would add my $0.02 as well. First off, Pulley rein is only for after the problem has already occurred, not a way to fix it. Not saying that with a horse like this you shouldn't practice it, but don't expect it to work miracles.
I agree with MIE, however a horse won't automatically know what you're doing unless you're in the alternative universe of "clincville". Amazing things happen at clinics, and then when you come home to redo it or try to pass it on then the magic gets lost in translation most of the time. I agree with everyone that said go back to basics.
If he's hard to canter....then work transitions. If he's good walk trot then use that. Trot large figure eights, canter a few strides through the diagonal then drop him back down to a trot or walk and reward the heck outta him. Don't let him get strong, ask for the canter allow a few strides and once he gets strong or heavy bring him back. Pulley rein, circle, whatever you have to do. Then start doing canter figure eights with simple changes. The circles will keep him slower and make him balance and the simple changes will remind him that he needs to downward transition when you ask him to.
Then add poles to your figure eight, then cross rails, then small verticals. Keep him turning, don't let him go for long stretches in a straight line, that gives him too much opportunity to get strong.
And I TOTALLY agree with Maura about that bit. If his flat work is good with the french link or whatever you said you use for w/t then use that to recondition him. Once he learns what you want and that bolting is not an option, you won't need a stronger bit and that elevator bit, especially with the converters on it is just giving him a lot to lean on and developing a tougher mouth on him.
I also strongly suggest that you consider taking private lessons from your pony club instructor or another instructor. They will be able to help you much more than we can. If that is not an option for whatever reason, please post video of him getting strong, bolting, jumping etc. The more information we have about him the more information we can give you to help you make him a better horse Good luck and keep us posted!