Your choices are grouped into a few different basic mouthpieces… unjointed, single jointed, double jointed, or multiply jointed. Variations on these are the width of the diameter of the mouthpiece, smooth or rough (usually twisted) surface. Then there are variations on the action of the bit in the horse’s mouth, leverage, or on the bars or on the corners of the mouth. Which you choose depends a lot on what your horse thinks of each, what he finds comfortable and acceptable. It sounds like your current bit is unjointed? Like a straight bar with baubles on it? If he will ONLY accept an unjointed bit, this is going to limit you somewhat, to other unjointed bits, which a straight bar mullen mouth pelham would be one of them. It is certainly worth a try, if leverage will help you. You have to try it to know. This will require you to learn to use double reins, which isn’t as difficult as it may appear. In decades past, young children learned how to do this as a matter of course- it isn’t a problem. Your coach will show you how to hold the reins. If you don’t like the double reins, there are other options… a kimberwick is a pelham with only one rein, and can be found in straight bar configuration or jointed. Pelhams can also be fitted with converter straps, which attach both the snaffle and curb rein together into a single rein. So if your coach likes the pelham option, that’s a start for you to try.
If your horse is towing, even if it is only to the jumps and not on the flat, it is a hole in his training. So he’s not as “broke” as you may consider him to be. If he was “broke”, he would hold his own pace during jumping training, because holding his own pace during jumping is something that we teach our horses to do in training. So this is something that you need to work on, treating this problem as a training issue rather than just a bit change. The classic option for a horse that tows is an old fashioned style of pulley gag, with two reins, a snaffle rein and a pulley rein, held together like regular double reins. This bit changes the angle of pressure of the bit FROM the bars, onto the corners of the mouth instead, when he goes to tow you. He can’t tow you from the corners of the mouth, he must put the pressure he puts on your hand onto his bars in order to tow you. So the bit defeats him, simply by changing where the pressure goes that HE puts on you when he goes to tow. These bits can be found with very soft and inviting mouth pieces of simple snaffles, and act as simple, soft snaffles unless the horse goes to tow. As he starts to pull down to tow, the bit turns in his mouth and pulls UP instead. He is immediately defeated, and can not tow. You do nothing, ride normally, soft hand, and the horse simply can not tow any more. Because this is a habit that he has acquired, that has worked well for him in the past, and suddenly it doesn’t work for him any more, the habit extinguishes itself in time. When he is no longer towing, and the habit is broken, you can usually move back to a regular snaffle again. Though many gags are jointed, there are straight bar options too. And since the bit does not “close” on the horse’s jaw bars like regular snaffles do, even a horse who prefers a straight bar bit can usually accept a jointed gag, if that is all you have or can find.