The link we both have to the litton shipyard ships they built have the delivery date listed. If you look for when the keel was laid (start of construction) it is much earlier. For example the USS Spruance DD-963 was delivered in 1975 but the keel was laid in 1972.
I'm curious about one thing. Having been to the litton yards in 1975 I know they had round the clock shifts going and I was wondering if anyone talked to the shipyard people who would have been working that night to find out if they had seen anything.