cant help ya here. Im right handed right eye domminant but it doesn't matter, rifle, bow, shotgun, pistol......I shoot with both eyes open can shoot either one, either handed equally well. I am probably alone on that one
I have the same problem but i have never tried shooting left handed, but a guy i know shot right handed for 30 YEARS just switched and he said it was the best thing he ever did to increase his accuracy. I would say borrow a bow and give it a try before you buy.