I still couldn't figure out exactly what I wanted to do next, but I figured I'd best do SOMETHING. And that something was stitch. Just stitch.
My initial goal was to stitch the background with enough white thread to mute the background a bit and help the chairs come forward. Though I haven't completely finished quilting, it appears my plan has failed. The thread just gets lost in the patter of the cloth. It doesn't tone down the background or highlight the chairs. The texture looks cool though, and that's an unexpected bonus. (Sorry about the coloring on the picture below; it looks very washed out. The colors in the picture above are true.)
But now I have two problems to solve. 1) Now that I've created all this texture on top of all the pattern, what do I do? 2) I still need to do something to amplify the whole piece and make it more interesting.