OK, without a Greek Advisor or Greek Life office, you are going to have to rely on Gamma Phi Beta to help you out. I think it's the only way. Gamma Phi Beta should welcome the fact that you want to bring more Greek Life to campus. I mean, being greek is not only about belonging to your organization, but to the greek community as well.
With that said, I would approach one of the Gamma Phi Beta sisters that you know well and are friendly with, and tell her what your plan is. I mean, they cut how many girls from their own group, and in true panhellenic fashion, should want as many women to succeed at joining a sorority. Ask them for a list of women who went through recruitment but did not receive a bid from them.
I wish I knew more about the campus, but unfortunately, if I were in your shoes based on the information you're providing, this seems to be the way to get interested women. Approach Gamma Phi Beta. They should welcome the opportunity to expand
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