Ah battleships. My first love when I was 7 or 8 and the love affair continues to this day. One of the finest days in my life was last December when I walked the teakwood decks of USS Alabama (BB-60) and clambered into the 16-inch turrets and 5-inch gun mounts. Hell, I went everywhere I could
I do think that if the battleships were recommisioned, there would have to be a great effort to reduce the manning levels of the ships. Not too much, mind you, because battleships are by their nature manpower-intensive. On the other hand, new technology like better paints and so forth should be employed (on ALL ships) to reduce the amount of chippin' and paintin'. A new point-defense system would be good, probably the new upgraded Phalanx Block 1B. VLS is also a good option to consider but I shudder to think of how and where it would need to be put in. The remaining 5-inch guns could hopefully be replaced by the MK 45 5-inch / 62-caliber with ERGM (if it even works), probably a total of 4 mounts would suffice.
I'm sure there are plenty of other electronic upgrades that can be used as well, although when it comes to the fire-control for the 16-inch guns, the 1940's-vintage "computers" work just fine. Although I wonder if there are/were/could be some modern electronic aids that could complement them