Hmmmm. I was kinda backwards to you. I shoot rifle left, but as a kid I always shot bows/slingshots right handed. When I got my compound, I wanted to go left handed because I just can't see squat with my right eye. I uncomfortably bought the left handed bow, and it took a little bit to get my form, but I regret it none. Perhaps already shooting a rifle left handed, helped me out, but my muscles strengthened up, quite fast.
I would reccomend if you try to go left handed, buy a cheapo, or go second hand, and see if you can build up the muscles, or like sheephunter eluded to, co-ordination,
to shoot efficiently.