There are other ways to join a greek organization. On many campuses it is called continuous open bidding (COB) or continuous open recruitment (COR). That basically means, that the semester after formal recruitment, if an organization has room for more sisters, they may hold events.
These events are usually very informal and give the PNMs a chance to meet the sisters and find out about the sisterhood in a very relaxed fashion.
I don't know if you have something against formal recruitment, but I suggest doing that first because it gives you a chance to meet women in ALL the organizations. Every chapter may not hold COB events and you wouldn't get a chance to meet those women.
Let us know what you decide!