I retrained myself with a target .22 pistol and a few bricks of ammo. I had to do it, for clay and bird shooting. My body wouldn't work the other way, so I had to retrain my eyes instead.
Many rifle shooters undervalue the body. But if you're really using your whole body, you can acquire targets better and faster with any long gun, not just a shotgun. So, simply being able to awkwardly hold a rifle on the uncomfortable side isn't a solution, IMO.
I shoot with both eyes open, generally. Since my left eye is naturally dominant, but I've trained to shoot with my right eye, I have a better idea of what's going on around me than if I closed my eye or simply used the eye that's looking through the sights -- even if I'm using a scope.
It's fun to play with this stuff.