When the bow was repaired, the undamaged upper portion was cut off to allow lowering the lower bow section to the hull which had been previously prepared to receive it. I've witnessed this myself on other ships at the Navy Yard. It would be very difficult, if not impossible, due to the space restrictions in a drydock that is virtually filled up with the mass of a ship, to lower a big section of hull to the drydock floor and push it in to fit the hull cut. I don't know if the upper portion that was fitted was the Wisconsin's or the Kentucky's but, since the Kentucky was being built at the Norfolk Navy Yard in the first place, it might still have been in the local area. All of those old shipfitters are gone now, so I don't know who to ask at the Yard. We have a technical library here but I've never used it. The info is there I'm sure. The difference in length is supposed to be only about three inches. There are some who claim that due to a building error, that the New Jersey is actually two feet longer than Wisconsin. But I don't know what the basis for that is.
As for the accounting of the discrepancy in lenght; I think that it was, indeed the width of the weld and the structure added to allow the two to mate. It is not just a matter of sticking the two pieces together and welding them up, there is a lot to the art of shipfitting and I respect the guys (and girls) who practice that trade.
This is from GlobalSecurity.org:
The Kentucky (BB-66) was built at the Norfolk Navy Yard, Portsmouth, Virginia, but never completed. Her keel was first laid in March 1942. Construction was suspended in June of that year and not resumed until December 1944. Work was again suspended in February 1947. The ship, completed only up to her second deck, was launched to clear the building drydock, so that USS Missouri (BB-63) could undergo repairs for damage received when she went aground on 17 January 1950. Though several schemes were entertained for completing Kentucky as a guided-missile ship, none were pursued. Her bow was removed in 1956 to repair USS Wisconsin (BB-64), and she was sold for scrapping in October 1958. However, Kentucky's engines remain in service to this day, powering the fast combat support ships USS Sacramento (AOE-1) and USS Camden (AOE-2).
BB-64 Wisconsin is allegedly three inches longer than the other Iowa-class battleships. This minor extension in the 887-foot battleship’s hull occurred, so the story goes, when shipyard workers placed the bow of unfinished Kentucky (BB-66) on to Wisconsin after her collision with the destroyer Eaton. As Wisconsin is three inches longer, she is the largest battleship currently in the world