Okay, I actually went to a panhellenic alumni website for another city in my state, and it provided contact information for rec letters unlike the other website did. I emailed the chapters by the emails provided and I will wait to hear back over the next week or so. I already have experience waiting for replies from alumni chairwomen and it totally makes sense considering it's summer.

I will just have to be patient! If they are not able to help me I will do what KD4Me suggested. It's turning into almost a hassle though! I've been scurrying around for a couple weeks now trying to get this taken care of and considering they are not required I'm almost starting to just give up because I'm wondering if it's even worth it at this point, especially since rush is in a month.