Put the rug by my front door, and the cats, immediately recognizing the presence of an item not covered in cat hair, worked diligently to correct it. Then installed the soap holder and shower curtain (easy).
Doing the towel ring was a bit more complicated, because of course I first had to remove the towel nub. It turns out that the remaining nub was attached more firmly than its mate (which broke off earlier). Surprise surprise...but a few very firm hits of the hammer finally took care of it. Now my bathroom floor is decorated with shattered bits of towel nub and plaster dust, but the newly installed ring looks very nice. What, clean up? Yes I suppose I could do that, but you know the cleanup is never as fun as the actual work.