I considered trying to machine embroider a quilt design in each set of four blocks but decided there might be too much of a learning curve. I'd still like to try that at some point, just not right now.
I finally decided to try stitching a design through the Golden Threads paper. Golden Threads quilting paper is a thin, translucent, gold-colored paper that is used as a no-mark method of creating a quilt stencil. It's available on a 20-yard roll in three different widths, and I'd guess it's available in most quilt shops. It's like tracing paper, but it seems to be more durable. I pinned and repinned the paper, stuck tape on it, rolled it and rerolled it, and generally abused it in the quilting process, and it never tore. However when I was ready to remove it, it tore off very easily and cleanly. It even came off pretty easily in those tight places where there was a concentration of stitches.
Here's how I did it. I chose a design from Electric Quilt's Quilting Designs series. After I drafted the log cabin into my EQ program, I imported the quilt design and sized it to fit my blocks. Then I printed out the design and traced several sequences of the pattern to create a small continuous-line pantograph. Next I pinned it to my quilt ready for quilting. Because the paper is translucent, I could see exactly where I wanted to position it. The pins poked me too many times, so I switched to double sided tape which worked just as well.
I used a walking foot to quilt the design, which meant I had to pivot the quilt round and round to stitch on my line. It might have been tedious except that I got pretty engrossed in it. I suppose you could do this on a larger quilt too, but if the quilt were too big it would more difficult to roll it up and maneuver around the needle. Free motion quilting would probably make it much faster.
This method worked so well for me that I'm excited to try it again, so I dug out the Pineapple Blossom quilt to work on, which will also measure 24" x 24".