I ran my swatch through the washing machine one more time – this time I just tossed it in with a load I was running. There was a lot more stuff in the washer, so the agitation was better I think, and it did felt down a bit more – from 9×12 to 8x11ish.
The stitch definition is still there, but not as noticeable at all, and gone entirely around the edges and corners. I also discovered why you put felt in a pillow case — I took it out, and my lovely blue swatch had picked up a lot of pale white fibers stuck all over it. They trimmed off readily enough with scissors though.