Dear maahey: I couldn't get anywhere trying to find the etymology of "chimes" meaning the barrel structure.And I have never seen a picture of the barrels the whalers used.
The wooden barrels still in use when I was a boy, had a larger diameter in the middle, and could be rolled without damaging a floor. But the shaping of those barrel staves was quite possibly depended on technology not available two hundred years ago; the staves have to be very accurately shaped. Straight sides were probably used on the whaling barrels, and both top and bottom mould have had to overhang.
Those barrel could not be rolled on a wooden floor without marring it. The barrels I saw as a kid also had metal rims on the top of the barrel, into which top fitted snugly. We used to get both potatoes and apples in such barrels.We had a "cold cellar" where they were kept, on north side of house, and heavy cloth over glassless window to keep out light, and let out excess moisture. Ah, the days of my youth, gone too soon!