Big kudos to fixyourownprinter.com's Epson Stylus Head Cleaning Solution. The instructions aren't perfect (they don't explicitly say "leave the printer on after dispensing solution), but the stuff works.
It's not perfect yet. The dump sponge (where waste ink is pumped during a cleaning cycle, and what caps the head so it doesn't dry out) is a bit oversaturated with ink and cleaning solution, so the heads are getting a bit contaminated with mixed ink, but printing a sample page clears that. By the time we get back from Glasgow, the head will probably be totally contaminated with mixed ink, but a sample page or two should clear that for good, and the dump sponge should be dry enough then.
On the really good side...
The Canon S450, which has been cranky and printing everything with a purple cast (the yellow head wasn't printing) was also cleared up with a dose of the cleaning solution. That one was a bit easier; the heads are designed to be removed by the customer, so I could pop the color head out, clean it, and put it back in. We're back to all the printers in the house working.