Just thought I'd update anyone who answered previously:
I've successfully obtained recs for 6 of the 11 sororities. I know having all 11 would be better and I am still actively looking, but I'm glad that I now have twice the amount of recs that I had when I started this thread.
Keep your fingers crossed that a miracle happens and I find the last 5 within a week and a half! (Though I know this is unlikely)
I also feel like I have a much more positive attitude toward the whole situation now. Rush is gonna be nerveracking as I've heard from a few people, but if it's meant to be then I'll get in somewhere.