South Dakota as an American R-class compromise

Was the 1939 South Dakota class essentially the American version of Britain's R class?

Potentially. It was a compressed North Carolina-derived design intended to cost less or enter production faster.

The 1939 South Dakotas have a plausible resemblance to Britain's Revenge, or R, class. The North Carolina class supplied the starting point, after which designers compressed the follow-on ships. The aim was to reduce expense or make construction faster while retaining a powerful battleship. This is a procurement analogy rather than a claim that the two classes shared the same detailed design.