FWIW: I have a brushed SS rifle that aquired several scratches, blemishes, etc. I pondered a good bit before attemping anything. Then one day I was at our local Ace hardware where I noticed 600 grit siliconized wet/dry paper.
It felt smoother than a baby's butt! I bought it and used it on the channel side of my rifle. I was careful to 'follow the grain'. It seemed to finish the barrel very close to factory, so I sanded the entire rifle..My barrel is also fluted and those flutes had a few smallish nicks in them. I wrapped a piece of this paper on a wood dowel that perfectly fit the flutes and worked it back and forth in the flutes. Bottom line: The rifle looks exactly like new. this paper removed any and all the scratches. Once again,,,,I was very careful to follow the original grain of the SS. I used the paper dry and used new pieces frequently. I'd do it again in a heartbeat. Ridicule me if you fellas wish,,it worked for me.