OK, so I got this solved.
When I took off diverter motor I discovered water, which meant the diverter valve itself was leaking upwards into the drive. New drive
and new diverter valve cartridge (thankfully not a diverter body replacement).
To replace (for reference in case anyone's interested), these are the steps I took:
1. Isolate electric and gas to boiler (technically the part is a water part, no gas parts were touched)
2. Isolate all inlet and outlet lines (CH in and out, cold water in)
3. Run the DHW tap until pressure drops.
4. Remove the diverter drive (remove clip, drive lifts off)
5. Unscrew the diverter valve cartridge from the top of the valve body and extract (I had a continuous slow water leak from the top of the exposed valve body - I don't think my isolator valve is entirely working)
6. Reverse the above to insert new valve cartridge and assembly drive motor.
7. Dry the system (kitchen paper), then replenish lost pressure in the CH by topping it up.
I tested it with CH and DHW separately, and now the valve drive works as expected. It moves silently, from one end to the other, with a satisfying little click at each end and no further movement.
Also, I tested the old drive terminals for resistance and there was Open Circuit across all pins, which meant it was knackered. The water must have damaged it, so I'm surprised it worked at all.