Social enterprise
You may want to consider setting up one of the forms of social enterprise. These are organisations that can be run by their paid workers (either collectively, in the form of a cooperative, or hierarchically, in other social enterprise structures). Social enterprises can be not-for-profit organisations by putting all their surplus income back into the organisation (rather than making profits for members or shareholders).
Your route so far:
Open group? No Workers in control? No Want charitable status? No Reinvest surplus? Yes