It shows a couple of differences from a Valjoux 7732, but is practically identical to a 7731 (which doesn't have a date wheel). So maybe Hamilton were adding a date wheel to the 7731 or perhaps early 7732s were a bit of a hybrid with some 7731 parts until production was fully underway.

Heuer used the Val 7732 themselves, in the "economy" watches of the early 70s. Same brochure as last time but a different page now!:

Don't worry about the "economy" bit, it wasn't the movement that made these watches cheaper than the "named" watches! If anything, the 7732 is nicer looking than the 7734 in the Carrera - the yoke-shaped bridge is much better looking than the plain, heart-shaped one in the 7733/4/6. And I'd say your Hamilton is a better-looking watch than those Heuers too - I'm not a fan of the case used for those economy models.

It does mean the watch could be a year or two earlier, though there's still a fair chance it could be from 1969 - my year of birth too, and I agree it would be nice to have a watch (or many watches!) from then. Unfortunately, however hard I try, attributing any of my Carreras to '69 would only be deluding myself! :/