Alright. So I got a message back from the Help Desk (finally) and they said this:
Thanks for your inquiry. Unfortunately we can only transfer groups to other admins in the group or to another member if the original founder contact us. Since there are no other admins I'm afraid there isn't anything I can do until the original owner of the group contacts us. Sorry for the inconvenience."
So it looks like we'll have to do without an administrator for a little while longer. Sorry guys.