It looks like there are a couple of alumnae associations around the city and the state that are fairly sizable. A short list:
North Shore,
Hinsdale,
Chicago Area,
Chicago NW Suburban,
Lyons Township,
Peoria
Bloomington
So the closest to you may not be Chicago. Check out this link to find the nearest one:
link Some of the chapters have an actual person to handle rec requests, some have a form, others I would email the president.
In the email (to whomever it may be) I highly suggest saying something like this:
"Although I have been able to secure letters to the other organizations, I am still need to find letters for Alpha Beta Delta, Zi Phi Chi, and Mu Nu Omicron. I believe they are members of (insert panhellenic name). Do you know who I could contact for more information?"