Actually, it seems very clear to me. You need a block that has the profile of the barrel. To get that, you wrap a chunk of 80 grit paper around the barrel, sandy side up, so the barrel turns into a metal sanding block with shape.
Then you take a block of pine or something similarly soft--maybe poplar--and sort of rough shape the reverse or negative shape of the barrel. Then you grind that block back and forth on the paper covered barrel, grinding the wood block to match the shape of the barrel.
Once the wood matches, stop, take the paper off of the barrel, and put the paper, or fresh paper, on the wood block. Now you have a sanding block that fits over the barrel and makes good contact. Sand away with increasingly finer grits of paper until you like what you see. Might stop at 180. Might go finer.
I'd been thinking about strips of paper and going at it like shining shoes. Makes the fine "scratches" left behind go around the barrel rather than running the length of the barrel.
Thanks, Taylor.