Ted, L.Brown,
I don't know for sure, but you might benefit from practicing with a patch over the dominate eye, if it is on the non-shooting side. I am naturally left-handed but shoot right-handed due to my right eye being dominate. I have shot several deer and squirrels left-handed with a scope which seems to mitigate the dominate eye problem. Maybe a 1x scope or red dot would help, with practice.
Mike