If you take 320 grit emery paper, tear it into one (1" ) strips, tightly wrap it around a flat piece of steel ( a fine finish file will work )
Then sand each flat from one end of the barrel to the other, do not work the sand paper across the flats, or round the corners of the flats. It will show up later.
Then use 600 grit paper, with a little oil.
In a short time all of the milling marks will be removed, and you will have a nicely finished barrel.
Wash with alcohol ( Shine), the drinking kind, 1/2 in you, 1/8 on the barrel, and the rest in you. Then you can either brown, blue, or let age.
If you wish to leave in the white, you may wish to age with clorox.
Best Regards
Old Ford