Okay, the 5A is implementedI haven't looked up the clearing curve for a BS 1362, 5A fuse, but came across this interesting article comparing 3 amp and 13 amp fuses, and learned a 3A fuse will hold on indefinitely at 4.5 amps. My guess is for a 5A fuse it'll be on the order of 7.5 amps.
Found a 330 µF 25v capacitor on the PC PSU board.Given this, my guess is part of your motor heating is a consequence of the supply waveform. If you have a largish (in the 100 to 330 uF range) electrolytic capacitor handy, temporarily clip it across the battery charger output, and see what happens. The motor ought to run cooler, and provide smoother low speed operation.
It was difficult to desolder.
The solder cooled instantly before the solder pump could work
... but got it out.
330 µF 25v capacitor across DC output
This had a similar noise reduction effect to the lamp across the dimmed mains supply.
IE. buzzing reduction
I then added the 40 watt lamp to the dimmed mains suppy.
The noise reduced even further.
It was already only a slight hum with the lamp (as per video), but clearly, both primary and secondary sides can be cleaned up.
However - having just wired it in the capacitor 'popped'!
So it failed.
This renders some of the questions (below) irrelevant at this time.
Q. Capacitor safety?
When removing the capacitor... should I simply short the two connectors across metal?
It sparks of course.
... but is that the correct procedure?
Q. Is the capacitor the superior option to Jim's concept of the lamp?
IE. should I solder it internally, and will it be fine for normal battery charging use?
Q. If the capacitor option works on the secondary side, should it be considered for the primary?
I have a large range of capacitors of varying voltages etc.