Me too
I have the same cross dominant symptom as the OP, over the years I have managed to train over it with handguns, I can shoot handguns with any hand eye combination. (with both eyes open)
With rifle it's a little different, I can shoot a light recoil rifle from either shoulder, on my left side I can shoulder the rifle and look down the sights/optics and it comes right in.
When I shoulder a rifle on the right side, I can see iron sights fine but optics are an issue, I simply cant see through the optics until I close my left eye, I have been trying to train this out for a very long time, I have never been able to get this part.
I have the same cross dominant symptom as the OP, over the years I have managed to train over it with handguns, I can shoot handguns with any hand eye combination. (with both eyes open)
With rifle it's a little different, I can shoot a light recoil rifle from either shoulder, on my left side I can shoulder the rifle and look down the sights/optics and it comes right in.
When I shoulder a rifle on the right side, I can see iron sights fine but optics are an issue, I simply cant see through the optics until I close my left eye, I have been trying to train this out for a very long time, I have never been able to get this part.