First, may sound strange, but coaching-wise, the dominant eye is leading for whether to shoot l/h or r/h.
So have you ever tried lefthanded?
That said, cross dominance is very difficult. I had a cross dominant rifle 'test-case'with my trainers exam.
He had a zero stance that was waaaaaaaaaaay off. (on the neighbours card).
Its very difficult to correct that with stance. Allthough pistol is easier than rifle.
I'd certainly block the vision of your non-aiming eye with a blend. Otherwise, your target will never be where you want it to be
Secondly, did you ever tést whether your left eye is dominant? Visibility is a good clue, but its not a test.