You are riding a TB, I presume an OTTB?
A TB who has been trained on the track, has been ridden and trained to take a “hold”. That is, to take the pressure of the bit on the bars of the mouth, and find his balance that way. It’s in addition to the gallop itself as an excercise for further fitness and strength, for his racing career. It means that a racehorse depends on this “hold” for his balance too. This is what we have to “reschool” when we change his training from “racing” to other forms of equine endevours. If this training is not adequately changed, the horse will continue to take a “hold” and “tow” the rider to high speeds, as he is accustomed to doing.
Since he is perfectly OK with taking pressure on the bars of his mouth without “backing off” that at all, some people may try “leverage” (your pelham bit) or bits that result in “pain” from taking this hold (twisted wire or other more severe mouthpieces). Sometimes this works, but often not. Because the horse will still “tow”, as he has done during his race training, because it’s all he knows.
Another option to try is to use a gag snaffle, with two reins… a pulley rein AND a regular snaffle rein. The horse can not put this bit onto the bars of his mouth and tow you with it, because when he does that, the pulley rein comes into play, and the bit runs UP in the mouth, which raises the head and takes the pressure OFF the bars, and puts it in the corners of the mouth instead. He can not “tow” from the corners of the mouth, so can no longer LEAN on you, and TOW you from the bars. Eureka, the problem solves itself.
This bit is not a “tough” bit, or a “painful” bit, it just works differently from a regular snaffle. The mouthpiece is smooth, and soft, just a regular snaffle UNTIL the horse goes to take a hold and tow you. When he goes to do that, the action of the bit changes, and negates what the horse thinks he is going to do, which is tow you. So he doesn’t, and the problem is solved. The horse is rebalanced, not so heavy on the front end, not so heavy in your hand.
As long as the horse does not start to try to tow you, the bit works like a regular broken snaffle. After the horse has got out of the habit on leaning and towing, is lighter on his front end and is using his hind end more effectively, you MAY be able to switch back to a regular snaffle… or maybe not.
I’ve used this system with many OTTBs repurposed to h/j successfully. One horse was a “confirmed bolter” on the track, and was galloped in draw reins with no direct snaffle rein (ARRRRGGGGGHHHH!), with multiple “evasions” developed after a 5 year racing career with multiple trainers. It worked. Horse had a long h/j career after reschooling.
Look around for a nice gag snaffle, set it up with two reins, a regular snaffle rein on the bit ring, and a pulley rein on the gag. Ride just like using a pelham. Give it a try. Good luck.