My oldest son is "very" right handed. And, he is "very" left eye dominant. He is 14.
His cross dominance issue is such that if he tries to close his left eye, his right eye closes also. Short of stapling his right eyelid to his forehead, we found an easy fix.
He shoots firearms left handed now after some practice. But, he prefers to shoot a bow right handed.
The easy fix.....He got himself an eye patch from the drug store for about $3. He wears it over his left eye. He keeps it flipped up until he is ready to shoot. Then, he flips the patch down, over his left eye. Thus, his left eye is open, but blinded by the patch.
I am not saying that this is the overall fix. Just a tip to try.
Hope that helps.