Very interesting indeed. It was a major concern for the US navy because all of their "fast battleships" were similar, North Carolina, South Dakota and Iowa. As the article said, the vibration was most severe at battle speed and the vibration effected the rangefinders which were critical for gunnery accuracy. I believe this is why North Carolina was known as the "Show Boat" because she was in and out of dry dock so many times for short cruises trying different prop combinations. It was a very serious problem for the US designers.
I also thought the South Dakota class had the skegs on the outside with the inner propellers shorter so the outside skegs would take a torpedo hit and protect the inner shafts.
Interesting stuff particularly how the beam was restricted due to the need to pass through the Panama canal. This was precisely the rational behind the design of the Japanese Yamato class. They estimated the maximum size battleship the Americans could design that could pass through the canal and deliberately built bigger as they had no such restrictions.
Cheers
Geoff