Matt,
I am right eye dominate and left-handed. I shot a compound with sights left-handed (right eye closed) then switched to shooting right-handed, split fingered, and aiming instinctively (both eyes open) with the longbow and recurve. I had shoulder surgery in the spring of 2008, switched back to left-handed last winter, and am currently shooting left-handed, three under (right eye closed), and using a gap aiming method. For me, both methods work fine but are entirely different, though I can shoot moving targets and quicker right-handed, but am more accurate at longer distances left-handed. It took a while to get used to shooting right-handed when I switched in the early nineties, now it is just starting to feel natural to shoot left-handed.
Whichever side you decide to shoot from, do yourself a favor and start with a light bow (35-40 pounds), develop good form and technique (use a video camera daily), and then ingrain the form and technique shooting at close distances (2-3 yards) using a blind bale.