Thanks for the good review, Mike!
Backing the bike up or pushing it in reverse won't hurt the speedometer, but driving it with a drill clockwise can, due to the higher forces involved. It needs to be driven in reverse (like unscrewing a bolt). I don't think it should be a problem for the gears, but it is for the hair spring which is a coil of brass. Running it in reverse tries to 'open up' the spring, rather than tension it.
As to the source of the clacking, if it's not the cable, my guess is the input helical gears.