Actually that very well could be it I don't have it with me but that might be it. And the one that is giving him cracks was his first bit hopefully not his new, though I have not ridden in his new one yet.
Put the new bit on his bridle, give his mouth some time to heel. Practice in the ring with just his halter, from the ground, giving to pressure.
Really you should practice all the ground work techniques, but particularly ones related to his head/face.
So stand with clip on reins attached to his halter, no tack on him besides that. The reins over his head, Hold one rein with just a tiny bit of pressure, so you can just feel his nose, and rest your hand on his wither with that much pressure. If he knows what to do he'll turn his head into the pull. But he may not. If he doesn't he may try to pull away, he may try to walk away, he may toss his head, just hold even, gentle pressure on that one rein and wait. Move with him so he's not getting away from it, so it's the same amount of pressure, just wait. At some point he'll try turning his head toward the pull, even if it's just an inch at first give it to him! Drop the rein, scratch his neck and tell him he's the most wonderful, brilliant horse in the world! Then do this again and again on both sides of his body and turning his head toward and away from you until he's bringing his nose to where a stirrup would be, with only the gentlest pressure on the rein. Then practice the same skill but with both reins, gentlest pressure, to get him to back up from the reins. Then practice getting him to put his head down, nose to the ground, with pressure on his poll (puling straight down with a lead rope).
People often over look the giving to poll pressure skill, because it's not vital to riding. But with a forward horse it IS vital to learn. When they're head is down they are relaxed, when it's up they're looking for danger. So getting him to be able to put his head down with gentle pressure can physically shift him out of flight mode.
I'd also work on practicing his ground yielding skills - yielding his hind end, front end, backing up and side stepping. Practice all these skills until he's really focused and listening to you.
This will give you good stuff to do while you wait a little while for his poor mouth to heal.
Then practice the same giving to the rein pressures you did with the halter with his new bit. Make sure it's a french link not a Dr. Bristol. Once he's turning his head very softly to his new bit on the ground practice at the halter from his back. Practice again at the walk. Use only the tiniest amount of pressure you can, only increase if he's ingnoring it (not doing anything) if he's trying to figure out what to do (tossing his head, pulling the wrong direction, ducking his head, anything) just hold the same gentle pressure until he tries the correct direction.