Cross Dominant
The cross dominant thing must be more common than I thought. I am also left-eyed/right handed. I agree that it is easier to train your non-dominant hand to work with your dominant eye. I shoot everything left handed, even pool. I still think I am right handed, though.
The pointing and closing one eye was how I always have figured which eye is dominant. I have tried shooting right handed and felt the same way as some others, why bother changing now? I think that it is important to figure out which eye is dominant because for me at least that eye has naturally tried to aim (hence dominant eye I suppose) and it would take some training to get the other eye to do it. Accidents that force you too switch are very unfortunate.
Don't agree with stance is overrated. Watching kids shoot in 4-H and stuff, the stance was very important. That was the biggest trouble my son had in the competitions and practice. When his stance was consistent and proper, his shooting was vastly improved. Archery really reinforces that I think. If your anchor point changes just a little you are way off. That has really helped my rifle shooting, learning proper stances in all positions.