Sounds like you're doing a good job of working out the meeting logistics.

If I may make a repertoire suggestion, start doing Carter Family songs if you are not already doing them. Most of the Carter Family's output is singable by people at any level. The tunes are easy to learn but interesting and distinctive. The lyrics are great. Try, e.g., Orphan Child, Keep on the Sunny Side, Distant Land to Roam.

As for "a format that will give all levels of musicianship a chance to participate"... I have been a member of a dulcimer club for 20+ years. The following works for us. We divide our meetings into two parts separated by a snack break. One part is a group sing. We sing stuff from our common repertoire as a group. This can be thought of as practice for our gigs, but we don't think of it that way. In the other part we systematically go round the circle and give everybody who shows up a chance to do something/anything. They can name the next song for the group to sing, lead the next song, perform a solo, teach a new song, tell a joke, whatever. The idea is to give people a chance to show off. A lot of nifty additions to the group's repertoire have come from this.