Something else. When you read what you find in the USS Basilone website, you learn that she entered the FRAM program on July 1963 and work had been completed on April 1964. Therefore, in about 9 month and that is no minor modification taking place during peace time (even if it was the cold war). You can't make me believe that US naval industry in the early 1990's and in war time would no longer be that capable.
I tend to have older ships put back into commission while I divide the time to commission all ships ordered from 1994 to 1996 by two. IRL, the last Arleigh Burke destroyer to be commissioned by 1997 was DDG71 Ross. In T2K, iy would have at least been DDG82 Lassen and more porbably DDG84 Bulkeley. When it comes to the Nimitz-class, the last to be commissioned would be CVN75 Harry S Trumman. You can even expect to have a number of San Antonio being pressed into service before the nukes fall.
http://www.uss-basilone-dde-dd824.org/history.shtml