Well I said I'd report back on this...
I suceeded in dismantling the printer, which was no easy task in the absence of a repair manual, but without breaking anything obvious. The plumbing all looked in good shape and well connected, so I proceeded to remove the heads. That was even less easy - I expected the head-assembly to unclip or unscrew, but actually it required bending back metal tabs that hold the guide rails. Ugly. I cleaned the heads pretty much as Ezzer suggested, with the addition of leaving them to soak in printer flush for 10 minutes or so (googling suggested that may help). Upon reassembly, the result is no different - no magenta. I optimistically tried some more printer cleaning cycles from the menu, but still no good.
One thing I noticed is that the printer-head assembly itself contains chambers for each colour, sealed with a transparent plastic membrane. After dismantling and cleaning, most of the ink had disappeared from these chambers - except magenta which was still full. I'm assuming that might just be confirmation that it's well and truly blocked, maybe by a bit of debris that got in when I was refilling the cartridges last week?
The whole job took about two or three hours including coffee breaks and frequent hand-washing. It's a horrid messy job with all that wet ink, and there's plenty of scope for doing more damage, so I probably won't try again.
Time for a new printer I guess. Thanks for the advice anyroads.