I am exactly that...Completely right handed, Completely left eye dominant. Have been shooting for years. Here is how i was taught and like to shoot. I shoot all guns right handed still. Handguns and rifles i have no handicap in shooting. Cant head to the right with a handgun, and left eye is perfectly aligned. Rifles, at the range I close my right eye and shoot, but in the field i keep both open, it is just a matter of focus. Being left eye dominant helps me keep one eye on my surroundings at all times. I have to conciously focus with my right eye or close my left eye. A shotgun is the most difficult, but easy to overcome. I have only looked down the side of my barrel accidentally with my left eye twice in the last 3 years out pheasant hunting. To me shooting right handed is much more natural, and i can FLOW with each moving shot and steady a lot easier than shooting lefty. This makes it easier for me to find my target while shotgunning. That said, i try to keep both eyes open while shooting my shotgun in the field, but it is hard. Most of the time i locate the animal with gun up and both eyes open, but then for a split second i close my left eye, center on target and squeeze.

That is how i do it. Probably not the best way, but it works very well for me.

Chris