There are several national service sororities. Have you looked into these? Perhaps, you can find what you are looking for there (strong emphasis on service, non-traditional students feel comfortable, involvement in the school, etc.) Starting a completely new organization is going to be hard work. If you do a search, there have been several threads about what is involved in starting a local. With a national service org, you would probably get more support and guidance with how to set things up. Plus, you would have a large national network of sisters.
Gamma Sigma Sigma
Omega Phi Alpha
Alpha Phi Omega (co-ed service fraternity)
Epsilong Sigma Alpha (i think this may be more of a community/non-collegiate sorority)
Delta Theta Tau (i think this may also be more of a community/non-collegiate sorority)
I know that are many more service sororities out there. These were just the first few results I got when I did a quick Google search. I would recommend reading through these and try to research other existing service organizations. If you truly can't find an existing organization that has what you're looking for, then look into starting a local. But thoroughly research the topic first.