Left-eye dominant, shoot right-handed. I just close my left eye... no problems.
Qualified expert with every weapon they put in my hands in the military... never missed during qualis with the M-16 out to 300 meters, 50 out of 50 with the .45, and I did miss once with the Beretta 9 mm (49 out of 50) -- have no idea what happened there.
used to routinely shoot dragonflies and swallows out of the air with my bb gun when I was little...
Ask the guys who've shot a few 3d rounds with me; I'd think they'd tell you it works out ok for me in archery, too.