The patch trick is pretty common.
I have the same I problem as you do OMO. My left arm and hand are retarted. There is no way I could shot a rifle left handed much less a bow. Luckly for me I can close my left eye without closing my left eye. I used to shoot both eyes open with one of those Sterner Duttera String Splitter peeps. I takes a lot of shooting to train your eyes to work together. With my current living conditions thats pretty much impossable. So I'm back to using my right eye only with a 2X2 peep.
I shoot a rifle right handed and just close my left eye as I'm shouldering so my right eye is forced to take over. Having a stock and good cheek wield make this technique possible.
I shoot a shotgun with both eyes open without a bead. I paint about an inch of the rib red on the muzzle end of the barrel without a bead.
I shoot handguns and pistols right handed with my right eye closed and my left open. I learned this technique from watching cross dominant IPSC shooters.
BTW Huck congratulations on finding a nice girl to date .