This is about the only realistic way to do this that I have seen posted yet.
So to make this a bit more specific, lets try this:
-BB-65 and 66 are never re-ordered as Iowa Class ships, both are laid down as USS Montana and USS Ohio but cancelled at wars end somwhere short of where Illinois and Kentucky were OTL
-Iowas are withdrawn from service on schedule in the late 50s following the Korean war
-Stalin survives about a decade longer with the result that around 1960 the Sovetsky Soyuz is completed as the first Soviet nuclear surface vessel, this apparent gap prevents scrapping of the BB-65 and 66 hulls (they lasted until 58/59 OTL, so not a huge stretch)
-Kennedy makes light of the "Battleship Gap" and commits to closing it with the Montana Class
-Montana and Ohio are heavily redesigned with nuclear propulsion, likely losing at least one, possibly both rear turret(s) in favour of helicopter and missile (Talos probably?) capabilities
-Both commission in 65-67 with guns canabalized from the Iowa class (which are never re-activated) and serve in Vietnam (not sure if any of the four survive as museum ships, but I suspect not if we're re-using turrets, one might get some form of BBG conversion for a while, but that's likely more a part of (nuclear) Montana development in much the role of Missippi in the 50s than a combat unit - if this happens I suppose this unit has a fighting chance)
-Sovetsky Soyuz retires at some point in the late 70s or early 80s being a one (or at most two) off ship with little real purpose and very much a Stalin era showpiece more than useful capability (I'd bet that OTL's Ulyanovsk is designated Sovetsky Soyuz TTL)
-Reagan's naval program gives both ships a refit in the 80s, upgrading them with some reasonable number of VLS cells and possibly AEGIS as a quasi prototype for the Strike Cruiser concept, being both more in need of refit and less size limited (if carrying fewer missiles) than the Virginia Class
-Retire either with the rest of the nuclear surface fleet at the end of the 90s, or if still in service in September 2001 (I'm thinking that while retiring alongside the Virginia's is likely policy the presence of AEGIS on a very capable gunfire and command platform might cause them to be the last ships pulled, keeping them around a few years longer) shortly after participating in the invasion of Iraq
-Probably both still in the reserve fleet today between the naval gunfire advocates politcal pressure and demands (with plenty of funding) for preseveration combined with the difficutlies in making museum ships of nuclear units