I managed to stitch the strips together in pairs, then just a few together to see what they will look like. I was going to do some sashing with more little squares, but I think it will be just fine without.
A lot of people asked what this fabric was -- it's "just hanging" by Alexander Henry. It's new -- I got it at my LQS last month (they had already sold most of the bolt last week when I stopped in). But I'm sure it must be available somewhere out there.