What about taking the pizza box swap to the next level?
..... and do it as a Round Robin.
When it returns to the owner, s/he will have a top ready to quilt.
You could give specs for each Round as to what they are to do to ensure that each layer does not become just another strip of fabric added.
Eg. add 3" pieced border; use applique; use HSTs .... etc.
The specs would also help give some guidance while challenging the monthly person to get creative, and perhaps step outside of their normal comfort zone.