Now that I've pulled it all apart, I can see part of the problem: the black plastic knob was actually "seized" onto the metal spindle (due to old age, crud, whatever - I know the feeling ). This meant that the only way for the knob to turn was for the metal spindle to spin in the arm which made it just loose enough to come off.
I've cleaned the spindle and the inside of the knob, so now I'll add some nice teflon lube and put it back together finding a way (probably glue) to hold the spindle-y bit in place.
Not quite up to RogerH's standards (I have no doubt he'd turn up a nice, new aluminium knob, and some clever, one-piece arm thingy all beautifully made and drilled for lightness, or something), but it should work for a while..
Still have to deal with the oil leak at the back of the engine, clutch friction plate, new rear leaf springs, probably a gearbox rebuild...but I will do (some of) that once the gravel roads have snow on them...