Unbuilt capital ships with a path into the missile age

What unbuilt battlecruiser concept might have remained useful into the missile age?

No unbuilt battlecruiser is selected. The answer instead favors the 1930s Lion battleship proposal and separately notes Alaska-class conversion potential.

The answer doubts that an unbuilt battlecruiser concept offers a convincing long career in the missile age. The 1930s Lion-class battleship proposal is preferred for its combination of speed, size, and firepower. Its 16-inch guns are presented as a possible basis for ammunition commonality and continued support alongside American ships. That is a proposed reason to retain the ships, rather than a demonstrated ammunition-interchangeability claim. Alaska-class large cruisers are also considered possible candidates for adaptation, with the distinction that they were built and are not classified here as battlecruisers.