I've read somewere on eye dominance in golf before, not sure though, its been a while. I am pretty much right eye dominant. I had a hard time with my terrain analysis class in college, trying to get the stereoscopic images to look 3D. My right eye wouldn't allow my left eye to pick up the other image, producing 3D image.
For me, i recently started putting with an open stance, but i keep my body square to my line. This allows me to look down the line more with my right eye, and able to align my body better. My front foot was throwing off my alignment in my putting. I kept standing over the ball thinking, "Im aimed way to far right". so then i would adjust over the ball, and things went to hell. I couldn't focus on my distance so that was off, and i would miss align putts by over 6", it was crazy. Since changing, i've been putting great, and my missed putts are just outside the hole, or just short of the hole dead center.
I never liked the alignment lines on the ball, for one, some greens are not all that smooth, so you put the ball down and the line would move. Also, i would be anal about getting the line perfect, so i would put it down, stand back, re align. It was driving me to OCD.