My $.02 worth...
If you are so adamant on creating a women's social club, rather than a sorority, I would respectfully suggest that you NOT use greek letters. If later, you want to affiliate with a national sorority, then adopt Greek letters which are meaningful to your organization.
When you say a women's social club... are you meaning that you wouldn't have some of the things that make a sorority different? ie. rituals, initiation, selective membership, etc. Right now it kind of sounds like you want to start a sorority with greek letters and just not call it a sorority because your school won't like it
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