We had independents in our house with no prob, although we didn't have a housing corp (we just rented from the landlords who owned all the sorority houses) so you might have a different story. Isn't your house fairly new? I think I remember seeing it featured in the Phoenix, or maybe that was Delta Kappa. Keep calling the housing corp until you get a straight answer, and I mean every day until they give you a yes or no. This is important.
If you do rent to independents, try to get the kind of girls who go home to visit the boyfriend every weekend or even older students or grad students. I know it seems like it might be a good source of potential members, but trust me that can get veeeeeeeeery sticky. It's better to rent to people who just need a place to sleep.
It is all 33girl's fault. ~ DrPhil