I don't think you have to retrain your eye to be dominant. You just have to train your eyes to shoot.
I am right handed, but left-eyed. However, for shotgunning, shooting off my left shoulder was not an option. I tried it, and my body wouldn't move that way. A lot of rifle shooters get away with awkwardly holding the rifle and adjusting with their arms; that's not an option for clay shooting. It's a whole-body activity.
What I did was take a decent .22 target pistol with big target sights that didn't cause eyestrain, and shoot brick after brick, purposely using my right eye. I closed my left, I left it open. I played with my eyes and focus. Finally, it worked. Now I can control which eye I use, without much trouble.
I can't say if this works for others, but it worked for me.