How about everyone in the group doing up zip-lock bags with small amounts of their fabric in each bag? If a block had to be appliqued, a 12 or 13" background piece would be included. And if pieced, say a few 6" fabric-of-choice squares, noting of course which would be the background. Left-overs would be returned to the box in case someone needed a bit more.
Or would you specifiy the whole group makes pieced blocks, or appliqued, or embroidered? I think a mish-mash would be great.
This is the first I've realized what a 'shoe-box' quilt was, and my mind is running rampant with ideas. Will put this idea to a cuz who has a machine/quilting shop.