@bbrock See I knew you'd come around on that patina thing.
Buffing wheel is the way to go.
Mine is just a simple HF bench grinder on a stand. The stand is the key since it gives you maneuverability. I also ended up turning up an arbror extension on one side to get more reach on big parts. Of course, a real buffer would be nice to have but you would be amazed at what I've polished on that cheap HF unit. Probably not such a big issue with these small parts.
The real issue is the need to keep buffing wheels seperated by what compound you've used.
You also want a variety of wheels. In your case you can skip the coarse sisal wheels that you might use for stainless steel.
I'd start with a loose cotton wheel and try White Rouge. That should be just enough to shine them without any scratching or serious material removal. You can always go back to something more agressive like Tripoli compound but honestly that is probably too much for chrome. Then you'll end up having to go back to White Rouge to get a decent polish and shine. Jewlers Rouge is even finer but will barely touch hard surfaces like chrome. And it will just make a mess by sticking in surface imperfections if the surface isn't already perfectly smooth. It's intended for soft metals; gold, silver, aluminum, etc.
Also you could use a sewn cotton buff with the white rouge that will give you an in between combination where White Roughe on a loose buff isn't agressive enough but where you don't want to try Tripoli.
My experience is that you typically need to buy 2 or sometimes 3 wheels to fill the grinder arbor and to have enough useful surface area. Because of the permutations of buff (sisal, sewn, loose) and compounds (Emery, Tripoli, White Rouge, Jewlers Rouge, Plastic Polish) you can see how quickly you build up a stack of buffing wheels.
Also buy a buffer rake. Fresh compound makes a difference in the end result.
You are pretty creative - could maybe rig up a way to do on the cheap with a drill in the vise and smaller wheels but to be honest, you really want the bigger wheels (6-8") to get enough surface speed on the wheel to do the work. Small 3" wheels held in a drill are for OK detail work but a PITA.