Hi Corina! amycat has a great idea (which is par for the course!
) I know even in good circumstances, there were women uncomfortable about doing "panhellenic relations." And there were some women who loved it.
I've seen campuses where the other sororities welcomed a new group with open arms and some where they were downright vicious. You never know until you try. I'm sure the Gamma Phi's will be somewhat uneasy, but on the other hand, they might welcome having another NPC around since the rest of the groups are local.
GOOD LUCK!!