What would you think of a row by row quilt? There would be a theme for each row like, Traditional, log cabins, wonky, pictorial such as flowers, etc. These would have a set sizes for each block & a set number in each row. Then for 1 to 2 months we would work on one row exchanging with others until our row was complete. We could even have a semi-set color theme or background color. Then the next couple of months we'd work on the next row.
This way instead of exchanging just blocks we'd end up with a theme quilt afterwards. Just an idea.