I would use two micro-fiber towels and some elbow grease first, just to see if it yields your desired look. However if you use an obital polisher, then buy a 3 inch wool pad and make that your designated metal polish pad. Wash it with some Totally Awesome and warm water. It should look almost new.
As for the rail and the screws, you can take out 3 or 4 in a row with know worries. Just look where the rail stops and starts and leave one in on either side of that point. removing a few screws will save you from having to dig the the paste out of the heads. You cant hurt anything by leaving them in but you will see a little fur from the wool pad.
If you don't have an obital, this is a perfect time to pick one up. Cable and Porter is my personal favorite but there are a number of manufacturers. Please do NOT use a dremal tool it spins way to fast and could burn the metal. No boo boo's please. If you're like me accidents happen and to often so use the KISS method.
"Keep it simple stupid" is my montra. LOL
I'll look at my model number of my C&P obital and post it if I remember.