The next step will be cutting the background fabric into long strips and sewing them down. Here is a better photo of the background, a brown batik:
The pattern suggests that the yoyos be sewn down with a running stitch and strong hand quilting thread, rather than an applique stitch. I have tested this and I like it. If I take the stitches between the gathers I can preserve the dimensionality of the yoyos, which will be nice. I'm really hoping that this next stage will be easy enough to do in front of the tv as well!