You guys do realize that you can train yourself to use your weak eye just as well as your dominant eye right? You can train yourself to write off handed, throw off handed, fight sowpaw, etc so you can do it with your eyes.
I've done it. In fact, since eye dominance is more mental than writing is, it is easy to do, but it does take a lot of practice. Fortuneately, you can practice it anywhere, anytime almost all of the time.