And this is part of what makes me question the OMG you absolutely positively need recs to every house theory. Possibly you don't, as long as you are open to every last chapter on campus. It's not a risk I would take, limiting my options over something as trivial as recommendations, but I still think you wouldn't 100% kill your options.
To state it bluntly - don't be a snoot! Happily accept the house you get, don't expect unicorns pooping rainbows - it's just a club when it comes right down to it, be willing to work for your friendships, and make the most of your college experience, in whatever form that presents itself. You are special. But you're not THAT special.
And IndianaSigKap, you know a Hawkeye has to rub it in anywhere she can. But think of it this way, at least you're not from Ohio State!