Personally, that sounds to me like he needs more training, not a stronger bit.
Here's what I'd do:
Start by just going around the arena changing speeds constantly, every few strides. Go halt/walk walk/trot trot/halt halt/trot halt/canter walk/canter trot/canter and everything in reverse!! Constantly change it up. The more you change it, the more he NEEDS to pay attention. But it's HUGELY important that every time he does what you ask he gets a complete release of pressure!! If he slows down move your hands forward and take ALL contact off the bit, not just a little. This says 'yes you did what I want' when he speeds up, take ALL contact off with your legs.
Then when he's changing up gaits with only light touches from your seat or reins and practically reading your mind, doing what you want the moment you want it, start throwing in circles, serpentines, figured 8s, do a circle then double back half way around it. Don't go a single time around the ring without doing something, either a change of speeds or a change of direction. By constantly giving him something different to do he's going to be hyper focused on exactly what you want. This forces him to learn how to predict what you want. Of course these skills will take time for him to pick up, the first few days you'll spend a while getting each request, but over time he'll get quicker and lighter on all his aids. So long as your releases are strong and obvious. Horses learn from the release not the pressure!
Once he's reading your mind, add a jump. Practice that jump, at each different speed. If he rushes toward the jump turn him away from it. If he rushes away from the jump spin him around and make him go the other way. NOT with force, but with quiet cues and strong releases. He'll soon learn that he can't just bomb over and past a jump careening around the ring, because you could send him in any direction, he needs to be paying attention to know where next.
Gradually add more jumps and ride him past a number of them without going over them, ride him near but not over some, then ride him over another he wasn't expecting, even going over one, then turning around and going over it backwards. Make it so he needs to listen to you. Try cantering toward a jump but 10 strides before switch to a trot. Try trotting after a jump then asking for a solid halt.
Point is change it up. The horse isn't paying attention to you either because the cue isn't clear or the release isn't clear- not because he needs something more intense in his mouth.
:) Have fun! Welcome to the forum! We love pics here!