I am also cross eye dominant. I draw the handgun so the sights are inline with my left eye, using BOTH eyes open of course. With muscle memory, you'll be able to draw and hit center mass at 25 feet easily under 2 seconds. Don't switch hands to compensate. Always holster on your "Strong" side, learn it, practice it & master it. It's not that big of a deal.
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you can also put a piece of frosted tape on the inside of your safety glasses blocking the dominant eye, this will train you to use the non-dominant eye to align the sights. you want to train to shoot with both eyes open, if you close one eye you lose depth perception and peripheral vision. after time your mind will automatically use the non-dominant eye and you can remove the tape.
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