Eye dominance really has no impact on which hand you shoot from. The bow string is lined up in the center of your vision at draw, not directly under one eye or the other.
I have been playing around shooting right handed, and other than I feel a little clumsy at first, the trajectory of the arrow is the same, its just a matter of building the same mucscle memory, and building those muscles up to match.
Glenn St. Charles switched to lefty, and I believe Fred Bear did too. My wife started out shooting right, but her right shoulder is weaker from a fracture several years ago, and switched to left with no problems. She has won shoots from either side.
It isnt as hard as it sounds, start out light and build good form, and go from there.