Well, firstly yes, these are cruisers. The US Navy has never had a “Battle Cruiser” in commission. These were very large (or “Super”) cruisers, designed with the purpose of overwhelming existing 8” gun cruisers (primarily IJN Nachi/Mogami types or DKM Hipper class). A look at the design shows that these are just up-scaled Boston class CA’s (hence the designation “CB” not “BC”).
An early rebuild of this class would parallel other contemporary cruisers, while later rebuilds would likely parallel the Iowa’s.
The Early (‘50s) rebuild would see the removal of the aft turrets (though the Mk38 may be retained it’s unlikely as this would be seen as extra room for missile space) & replacement by missile systems, most likely the Mk 4 Terrier system due to the extra volume available for vertical loading, though the Mk 10 or 12 Terrier/Talos systems may be used instead. The forward turrets would (hopefully) be retained (including the Mk38 – while the replacement for a Mk42 or later 45 sounds cool, the Navy would never spend money on it as it doesn’t enhance firepower significantly to justify the expense, actually the modern CGN Long beach received a modification to give her NGSF capability by adding 2 surplus Mk30 5”/38s amidships, it’s not likely they would add a weapon system to one ship while replacing it from another older ship & the labor intensiveness of the Mk38 is not an issue as these are large ships designed for them anyway). All 20mm’s & aircraft facilities would be removed. The 40mm’s may be retained initially (as with the Iowa’s in Korea) or replaced with Mk33’s. She would probably retain 2 of the 4 side Mk38’s & replace the other 2 with Mk11 Tartar systems, whether the 2 forward of aft Mk38’s were replaced is unknown, they could go with a full guns forward/missiles aft configuration or have some of each in each location (the Mk11 was fairly sturdy &7 unlikely to be effected much by the 12” guns {as long as a bird wasn’t hanging from the rail
}). The upper works would be rebuilt (as with most CA/G conversions) with upgraded radar & missile FC systems (probably the SPG-55) & a large command center where the hanger was, with extensive facilities for fleet command staff & very long range com systems, also likely additional Mk33’s where the catapults were (the addition of extra Mk38s here would be cost prohibitive due to the lack of below deck magazine space). No Mk16 is likely as these are not ASW ships (it may be added to support ASW capable ships but I highly doubt it & it would likely be removed quickly as being redundant).
A 80’s/90’s upgrade could have 2 versions (cheap or full like the Iowa’s) the Full conversion would likely be close to the Iowa full conversion, with the removal of all old missile systems. A full hanger & flight deck built up aft. Mk41 added in the former aft magazine spaces. The upper works cut back down with modern electronic, Mk15s added & a platform added amidships for Mk141/143 launchers (adding Mk41 here would be very unlikely but adding above deck launchers for Harpoon & Tomahawks would reduce the space needed in the Mk41 for these missiles & allow more room for other types). & Mk 25/29s in place of the Mk11s (or removed to make room for a “ski jump” along the side if aft mounted)
A cheap conversion would see the same rebuild of the upper works (as with the Iowa’s) but would retain the existing missile systems (if Mk10/12s & Mk11s or replacement of the Mk4s with Mk26s). No hanger added. Mk33s may be retained, removed or reduced in #. It’s unlikely these ships would use Mk13/22s though the Mk11s may be replaced by them (likely 22s due to limited space to the side) or Mk25s. An interesting idea though might be to replace the aft mounts with a triangle of Mk13s, 1 in the former Mk38 position & the other 2 side by side (if there’s room) in the 12” position.
A modern upgrade could see the replacement of the Mk11/22s with Mk29s, Mk49s or a small cell group of Mk41s. the forward Mk38 may also be replaced with a Mk29/49, or an AGS. The other 2 Mk38s would likely be replaced by AGSs as well (or a pair of Mk71s
).