Rusty Rivets

Your local hardware store will have a section for welding supplies. You will find small wire brushes there. They look like nasty toothbruses. They should have small thin metal bristles. You can use them to knock off the rust on the rivets. Brush the reed plates length-wise, at a 90 degree angle from the slots. Don't brush them in the direction of the slots. On the draw reed plate you will brush at a slight angle to follow the rivets. 

You can follow this up with a standard toothbrush. First cut down the bristles on the toothbrush until they are a little less than 1/8 of an inch long. Then brush the reeds again with this modified toothbrush the same direction you used the wire brush. You can use a little mild dish soap and rinse well. this will get rid of all the loose rust.

After the reed plates dry off, you can coat the rivets with chapstick to prevent more rust. Wipe off the excess and you are done.