Oh, well, not crazy easy lol
The right diameter flapper wheel on a dremel might be a possibility, if you're looking for power tool option. But would be difficult to do evenly, as you said.
To do by hand I would try to find something to wrap sandpaper around. If you can't match the diameter perfectly, go slightly undersized and softer.
Cork works well. Firm, but not hard. Just enough give that it will spread the pressure a bit. Unlike a hard dowel rod that would only sand right in the apex of the curve
Orrrrrr.....sandblasting/tumbling, then buffing?
Or, if you just want a shiny surface, and don't care if there are bumps in it from the milling, look into "rust erasers". They won't be tough enough to sand siren the mill marks, but they will clean up the surfaces.
Use them to follow the "grain" of the mill marks, working your way up through a few grits, then final polish with a paste polish on a soft sponge that can get down into the grooves.