Hi
there is a liquid that used to be available in this country called MICRO, unfortunately it is now only available in bulk to laboratories but it is a standard lab cleaner used to clean test tubes etc. you just add a couple of capfulls into a bowl of hot water, soak your cases for a while and then wipe the gunk off as you take each one out. Rinse in cold water and allow to dry, brilliant stuff. I'm sure you will be able to get something similar from a chemical supply warehouse.

Failing that, if you have access to a lathe, turn some tapered mandrels, chuck them into an electric drill, slide the mouth of the case over the taper and away you go, any metal polish on a piece of old rag will bring them up like mirrors but be careful not to let the rag wrap around the case or it can give you a nasty knock. I used this method for years until I bought a tumbler.