Thanks for the thinks & links, folks.

I'm going to reverse the rug so that it sits in the light of a window. I'm raising it off the ground a bit. I'm setting a fan on it. Once I've done that for a while, I'll scrub the discoloration and see if it stays off.

If not, the garden mulch thing isn't a horrible idea. Makes for a pretty stylish garden, what with my garden being half perennials and half discarded pottery seconds.