Changing the barrels is very much an in-port job. The barrels each weigh about 100 tons, and handling objects of that size and weight on a ship at sea isn't easy. A short description of the barrel-changing process:

Before a regunning can be started, shoring must be placed between the two decks below the main deck. Then on the top of the main deck shoring must be built up to hold two rails paralleled to the barrel. Next the barrel is disassembled from the breech and yoke and slowly pulled out of the turret while riding on three specially made cars on the rails. When the barrel is all the way out of the turret, it is lifted off of the cars and the new barrel placed on the cars and the process reversed.

pg 22 in Arthur R. Romano, "Reactivation of 16-Inch Three Gun Turrets In the Battleships", Department of the Navy, 1987: http://dtic.mil/dtic/tr/fulltext/u2/a183947.pdf

A film showing a barrel being moved by road: https://www.youtube.com/watch?v=8iJveCclXfk

Once the barrels were changed, they were re-lined, and could then be re-used. Romano (1987) gives a description of the construction of the barrels, and re-lining.

A barrel life of 344 shots might not seem like much, but that's 3 full ammunition loads - the Iowas carried about 130 rounds per main gun, which is a lot for a battleship (the average is closer to 100). The Iowa fired about 12,000 main gun rounds over service life, so needed multiple barrel changes. However, those can be done between operations, and often can wait to be done between wars (at least some of the Iowas used in the Korean War got through the war with a single set of barrels, having had fairly new barrels at the end of WW2).