I also used my ship creator to re-calculate all the ships and add a few more. I Added the Tribal Class Destroyer, Hood, Renown, and Ark Royal for the Brits. US got the Fletcher and the Yorktown. I added the the Japanese; they have the Kagero class destroyer, the Agano class light cruiser, the Mogami and Tone class heavy cruisers, the Akagi, and the all powerful Yamato.
Based on my methods for stat generation, the Yamato and the South Dakota look like they could go toe-to-toe. The Dakotas quality construction, protection scheme, and fire control balancing out Yamato's brute force. As a bonus the Dakota has almost 3 times the AA output as the Yamato.