I tried the correction for cross dominance...

[Jeff22]

I am right handed and have a left dominant eye.

When shooting pistol, I found that I could line the dominant eye up with the sights merely by turning my head to the right slightly. Since I shoot from the Chapman Stance (a modified Weaver with a nearly locked right elbow, this worked out pretty well. I don't know how well it would work if you were shooting some variation of the isoceles.

(When shooting long guns I shoot off the right shoulder with the right eye, and close my left eye)