If your org doesn't meet the guidelines to be recognized by campus that will cause many hurdles in advertising and recruiting new members.
Honestly, I'm in a co-ed fraternity. It's the most fun I've ever had--seriously. I love it. We have ritual, initiation--we're like every other greek org out there.
Maybe you could charter a chapter of Phi Sigma Pi because we are not at all affiliated with the social greek system. But, our main purpose is to foster fellowship among our members. (
www.phisigmapi.org)
What about service orgs? They are not affiliated with the social greek system either. There are many service sororities out there. I know of Omega Phi Alpha and Gamma Sigma Sigma.
I would talk to your student activities office again and find out exactly what they define as "greek life" because there may be many loopholes that you could take advantage of.
Unless, of course, you really want something just like NPC.