Today's progress is - I finally have a 4-speed fan, rather than the binary on-or-off option I've lived with for almost 4 years!
As expected, the culprit was the resistor pack. For those who will no doubt come after me and repeat this job, I found it distinctly easier to access via the removable panel at the back of the glove compartment than in the "Lotus Position" (lying on one's back with head in the footwell). That said, it still wasn't exactly easy to reach...
The resistor block is part 19 on this page if you have access to the parts manual, but it doesn't really show you very clearly where it fits.
Stick your hand in round behind the blower motor, and on the top you will find the resistor pack. Follow the wires to lead you to it. Disconnect the wires (you need to find a plastic clip on the connector to press down before it'll come off). The good news is the resistor pack is held in with only one cross-head screw. The bad news is that it's a bugger to undo, because there is limited space above the screw to fit a screwdriver. The best option is probably one of these:

but I didn't have one, and I lost my stubby screwdriver so can't confirm if that would fit. I have a screwdriver with an extendible flexible shaft, but that's not flexible enough. I succeeded by using the screwdriver bit from the flexi-screwdriver; combined with pliers I could make a half a turn, and after that I could unscrew it using the screwdriver bit alone.
The BAD news is that they do not make the resistor pack A089P8047F any more - SJ Sportscars list it (for a pricey £73.01 +VAT), but when I tried to order one Steve replied that it's been obsolete since 2011
Fortunately Lotusbits would sell me one, but only attached to an entire blower assembly including the housing, fan and all. So I now have an entire blower assembly, minus resistor pack, if anyone could make use of it?
Comparison between my old resistor pack and the replacement:
How on earth did my old one manage to get in such a state???
Installation is the reverse of assembly (to quote Haynes), being very careful not to mash the exposed wires as you slot it into place.
I did try measuring the resistance of each coil with my multimeter, in case anyone in the future felt motivated to re-wire their existing resistor block. I got readings of around 1.0Ω for each coil, but with such low resistance it was difficult to get a steady and meaningful number.
I hope this proves useful to someone some day.