I think if it were early 60's it would have Universal brakes, a cottered Magistroni crank and a Cinelli, not Campy headset. Also I'd expect Cinelli steel bars and stem.
I agree with your dating it from 1963-1968, but would point out that the brakes, front derailleur & stem have definitely been updated. Therefore, the components are not necessarily as old as the frame, and of limited value in dating it. I believe the bars, stem & brakes were put on later (maybe they came together from another bike), as they are all 1970ish parts (give or take a few years). The 1A stem has a recessed pinchbolt nut which dates from the mid 70s, while the brakes are flat QR NRs (with later shoes) which means they could be a bit earlier, but they aren't as old as the frame. The front derailleur is also from about the same period, as it has a retaining circlip, making it a 1973-77 Record (according to Velo-base, as well as my own recollection). As you pointed out earlier, the lack of holes in the lugs, as well as their style are the real clues to the frame's age.