Some people say they can shoot cross-dominant and it doesn't matter. Maybe they can, but I just can't wrap my mind around it. If that actually is the case, then it shouldn't matter where you draw your bow to and anchor.
Your dominant eye is the eye that is pinpointing a straight line to the target. That's why a typical person wants an anchor point that puts the arrow directly below the pupil of the dominant eye. Otherwise, the arrow is pointing at an angle to the target when at full draw.
I recently discovered that my 9 year old son, who is right handed is left eye dominant. He's been shooting a bow right handed and always cocked his head kind of funny when he was at full draw. Now I know why. He was automatically trying to line up his dominant eye with the arrow. So I had him switch to shooting left handed and with the arrow resting on his knuckle rather than on the rest. It was a little weird for him at first - even the action of nocking an arrow left handed - but once he got on to it, his form improved immediately and his windage on shots greatly improved.
If I were you, I'd give shooting left handed a try.