I've been using products from Caswell Plating for years. First for powdercoat then for polishing supplies. I used to build engines and had a bunch of "chromeboys" locked in a battle to out shine each other... I spent a lot of time polishing bolts, cylinder heads, everything you can think of.

Recently bought a combo kit (different sizes available depending on buffer size and HP rating) with several wheels, compounds, and a rake. It comes with a polishing guide to walk you through the process and get you started.

The shooter rod handle -should- be solid aluminum, so some sanding to get past the pitting and then polishing to shine it -should- work. Do you have a similar one to practice on? That would be the best bet, just like soldering, practice on something disposable to hone your skills.

The shooter surrounds are chrome plated, so you can remove the plating if you go to far. Living with minor pitting or replacement are the only easily attainable options. You can strip the platings, polish, and get it replated, but it'll be very time consuming and expensive.

Same for the coin door. I believe they are chromed as well. Any rust coming through means the plating is comprised in that area. You can steel wool it to remove the rust then polish it over to reshine the are, but the rust will come back