Grille cloth: see if you can find a dry cleaning spray can called K2R. It's dry cleaning solution with chalk in it. Shake it up, spray it on, let it dry thoroughly for half an hour. The solution dissolves the dirt and the chalk soaks up the dirty stuff. Then you brush or vacuum the chalk off. Remove speakers first. If you can't find that you could try a spray foam upholstery cleaner. Before I used anything I'd try it on a little spot to make sure it wouldn't hurt anything.
Thinking about winding coils I remembered this video a guy made using a coil winder. The winder is really neat but what's neater is the trouble he went to making the video, coordinating the music right down to the scissors snip etc. I wrote and told him so a long time ago.
http://www.youtube.com/watch?v=FIOocMoRsYQ