You might try using the bit you ride with, when you drive him. See if he is responsive, will stop when asked to, if using it. He will have a lot less aids in driving, than he does ridden, so that could take him a bit of getting used to in his responses to voice and reins only.
When folks say they want “a Myler bit” I have to ask what design mouth and cheeks, before I could recommend it for what they want to do. While the brand name is good, they have MANY kinds of bits to select from. Not all of them will give you “miracle” results, because they are almost exactly the same as other makers provide, for a much lower cost. Though you will have to hunt a little for a 6.5 inch mouth! Most of our horses wear 6 inch mouthpieces and I know how hard they are to find!
I have purchased a couple Myler bits, with what I think is the Comfort Snaffle mouthpiece. The mouth gets solid with a port when both sides are pulled equally, but the “magic hinge” in the center allows one side to be lifted and used independently of the other side. No folding of the mouthpiece. Husband is going to take the rings off, put on shanks, so it is a curb bit for riding. The independent hinge is pretty useless, if you can’t lift one rein, for showing horse what you want, so probably not my choice for driving. No lifting one side with reins run thru terret rings on the shoulders!
I got the 6" mouths with ring sides for about $70. Husband is a skilled metal worker, will put the shanks I want on that mouthpiece, instead of paying the usual $150+ and waiting time, for a customized bit with shanks in that size mouth. Just something I want to try on our horses because the action is so very different with the independent sides.
I probably would not be buying any other Myler bit mouth type, since I can get almost all the same ridden results with other bits I own. So my suggestion is to go ahead and use a bit he has now, see how it goes with ground work first. Make sure he responds to that bit, is under TRUE control, before hitching him with that bit. I would not jump in, buying a fairly expensive bit, totally new style mouth and sides, before exploring my other options in bits I already own.
I will say that our horses are all expected to finally go in leverage bits. To us, that is what finished horses wear, in the ways we use them. They are progressed from ring sided bits, up thru other bits, before they graduate to the more traditional Driving bit styles with cheeks. We never need to set the reins down very far for control. Most go on Rough Cheek or First Bar (the slot right under the mouthpiece) so they just barely feel the curb chain. It is all they need, because they have been TRAINED how to work with a curb bit, understand how to give and take when the reins are talking to them, not forced into “a headset”. Does take time to get that, build the muscles needed for self-carriage to go comfortably when collected.
We find it easier to develop a horse for going on into a leverage bit comfortably, giving the right responses, than to keep fighting how direct pressure Snaffles (various mouthpieces) don’t work for him. Snaffles have FINALLY gotten a lot closer examination of how they work on horses in use, and Snaffles are NOT always the gentle, kindly bit envisioned by many over the years.