Instead of removing the rust, just remove the screw, source for a new set of screws (and remember to buy extras in case they rust) to replace the old ones.
A little trick is to spray a thin layer of lacquer over the screws and dip them in wax to provide some lubrication.
Hope this helps, and btw the screws you can find at DIY stores or hardware shops.
1. use a flat blade screw driver (rather than a cross blade) and tap it into the damaged head of the screw with a hammer so that it seats properly and then try turning the screwdriver leaning on the driver.
2. put a drop of superglue on the damaged head and hold the screwdriverr in place waiting for the glue to dry (30 seccondds) then try turning the screw driver leaning over the driver again (this extra weight will help the driver grip).
When they are out, get a new set of screws from Davis or a guitar shop and keepthem clean.