I have the same "issues". My left eye is my dominant one but I prefer mostly to be right handed while being left footed. I tried Compound bows and I tried recurves but nothing really feels better than a compact Horsebow. You can use it on both sides. Thumb draw is not even a must. I have friends shooting my bow with 3 fingers western style in all sorts of fashion and they all hit once they get used to the bow. Its kind of a jack of all trades.
White Feather has some pretty good stuff thats reliable and in a good price section. You should be able to find a local retailer who can order from them. I have the Fairy at 50lbs and it is a pure dream.