RE: Right hand left eye.....
I disagree but as you can tell by other posts (and my last line), the human body can adapt. I found out I was left eyed at an early age (7) and my dad had me shoot left handed from then on. The key word here is "dominant" where your left eye is going to always want to take over in aligning your sight. If you can get over that you'll be fine.
Personally I find it to my advantage to have my strong arm (right) holding the bow steady while pulling the string back with my weaker arm (left). I never had a problem with left arm strength either.
However what is ironic is I recently had a left shoulder injury and might have to switch and shoot right handed if it doesn't heal properly. I'll have to change my Login name!!!