RF,
First off I need to tell ya I ain't no expert! I am left handed and a relatively new bowhunter. I had to decide how I'm gonna hold the bow and stick with it. If I put a death grip on the bow, I shoot left. If I try to do the open hand style,like my youngun, I shoot right. If I hold the bow with my entire hand, without the deathgrip....THUNK! Dead center! I had to tighten my bow strap just a bit too.
Another thing to consider is your peep. Is it coming back exactly the same way, to the same place, everytime? If it's canted one way or the other, or ya have to move your head around to find it, this is gonna cause ya to shoot off too.