Flood,
I am right handed and left eye dominant. I shoot left handed, it is a little harder to get used to, but I shoot twice as good now than when I shot right handed. I started shooting a longbow right handed at age 5, and switched when I was about 28, so I had 23 years of training to overcome. The beauty of switching is that I got away from several bad habits.
Good Luck, it can be done, and is by far the most effective way to do it. Also, you'll have a bunch of right handed bows to sell.
Blake