I am also "cross-dominant", of sorts. I am ambidextrous, but mostly biased to being a righty. I went through elementary schoool as a lefty, but was switched over to righty because I kept dragging my hand through my writing, smudging the pencil all of the time. I am still left eye dominant, but play golf as a righty. I can, and do play hockey and baseball either way, and actually have more power as a lefty in baseball, but batting righty lets me choose to hit off-field at will because my dominant eye is closer to the ball when it comes to the plate and I can get a better bead on it. That's my theory, anyway. I switched over to left hand low for putting last season, and I have seen a remarkable improvement. In my mind, I think it helped to get my dominant eye over the ball more....or maybe not, but it works for me.