Your calculations reveal how much too big those 1/350 parts are indeed... The Terrier Missiles are from the kit, but they are oversized as well.
The Gun Director on top of the bridge should depict an AN/SPG-53. To my knowledge, those Farragut-class destroyers did not have Mk37 Directors fitted.
As soon as I am back from my trip to the States I will look at some SkyWave parts I have laying around somewhere... Thanks for the hint!
Best wishes sent from Ridgway Hall at the Army Heritage and Education Center, Carlisle, PA.