Sweet bike!

I would agree that the bike is no earlier than 1963, the other components match the dating. Take off the locknuts on the hubs, flip them over and you will see a date stamp. Also, Campagnolo introduce a new headset in 1965, that could give you a clue, check the timeline for details.

As for the crank, I don't know enough for a definative answer but I would guess Record would be the way to go over Nouvo. (Strada is just a designation instead of Pista, you don't want the Pista).