Well, blocking definitely helped. I found the best result was to purl very tightly (give a little extra tug to tighten each purl stitch). Of course, then the cloth comes out more rectangular than square, but I just stretched it under water while soaking, then blocked it out. You really have to press down on the stockinette to get the central image to stand out.
While doing so, I wondered about the design. It is basically a backdrop of stockinette, with a purled image in the center. Is there a stitch other than a simple purl that would stand out (up) more against the stockinette? I could not think of one, but I am sure there are some experts here who could!