The 'before' photo: a very dusty tangle of wires, bells and woodwork. 

First step is to get the worst of the dust off with brushes and compressed air:

After polishing each set of contacts with some fine wet-and-dry, amazingly all seven sets of coils still work fine! Passing ~0.5A causes each hammer to waggle, which would strike the bells if I hadn't removed them for cleaning.