Due to personal time constraints I have very little exposure to group quilting.
The two different groups that I was a part of for a short time, one was everybody bring your project on the specified day and each work independently while visiting with one another.
The other group was primarily non sewing folk but was focused on creating banners to be hung in various places around the church. The organizer had specific tasks that individuals could do - for instance, trace around appliqué pieces and cut them. Then others arranged and pinned them on the backing. Someone else had ironed the fusible beforehand. Seemed to work nicely. I think they did a different banner each meeting until they had all of them done. They were also going to do pieced charity quilts and one lady had the pieces cut ready to sew if anyone wanted to work on that.
For the group you are talking about, I can see how you could have the newbies first cut the squares (or strips) to be used, then choose the ones for each set, and teach them how to sew them together. That way they can be productive very quickly and learning at the same time. Also if they don't all have sewing machines, they can rotate tasks so each has a chance to do all parts of the process, and the experienced ones don't end up doing all the sewing. Yes you experienced ones do end up as teaching the 'class', but that's part of sharing the love of quilting.