While getting some other things at a craft store, I came across a kit for providing an iron rust finish to any surface. Put on a layer of iron-bearing paint, then squirt on some kind of rapid oxidizer. I thought "Hey, I should print something out for this." And so I did. And this is what I got:
Not bad, I think. It's lightweight plastic, but I'm afraid to drop it on my foot.
The dragon-head door knocker I got off of Thingiverse was, in the event, really hard to treat. It's a very complicated shape, with lots of little nooks and crevices, and both the primer and the iron paint were quite thick, so it was difficult getting it completely covered. The "activator" sprays on, though, so that wasn't a problem.
There was also a problem with printing. The design is perfectly good, but my printer kicked out about an hour before finishing the job. I'm guessing a power fluctuation on our old wiring or something. Anyway, I was able to measure the height of the printed portion with the digital micrometer, fire up netfabb, slice off the unprinted section from the design, print that part off, and superglue it on. It went much better than I expected, and I can't find the seam even though I know exactly where it should be.