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. 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).
Some funders are unwilling to give grant funding to social enterprises if some or all of the directors are paid. If this is a concern for you, you may want to go back and answer No to the question about the group organisers being paid, or choose a structure where there is an unpaid committee and paid workers who are different people.
Your route so far
Open group? Yes Flat structure with no committee? Yes
Organisers paid? Yes
Reinvest surplus? Yes