So, after 6 weeks of fogged-up windscreen, last weekend it was time to remove the fan (again) and do a better job. I can wholeheartedly recommend the use of a 7-year-old for this process, they fit in the Lotus Position under the dashboard and can manouvre their arms far better than I can.
First job was to remove the fan:
If you have the same problem I originally did, this should be as far as you need to go. Some lubricant where the shaft passes through the housing should be all that's required.
This photo shows what I found when I unscrewed and removed the motor cap. Clearly my messing around before led to the brushes coming out of their guides, so the lack of rotation was no surprise:
The next photo shows everything disassembled. On the left is the rotor. The plate holding the brushes is next, the springs should live in the guides pressing the brushes against the commutator on the rotor. The springs were different lengths - I've no idea why, the guides were the same depth, and there were a different number of coils so it's not just that one spring has got a bit more depressed. The ring goes on next (flange facing towards the rotor), to hold in place a sort of felt bush. This is all the support for the rotor at this end, and was shiny with what seemed to be copper-slip, so I just applied more of the same when I re-assembled.
Plenty of wear still left in the brushes, so now it's re-assembled it should be good to go for a few decades more!