I cropped them a bit Bo, hope you don't mind.

The case looks like a Heuer 3336 - that swirling curve on the lugs is the giveaway for that one. That would tie in with your recollection of the movement too, as those use the Valjoux 22. They also have this style of polygonal caseback.

The dial, though it doesn't purport to be a Carrera after all, I think is still a problem. I can still see some of the ridges in the 30 min register and the markings there look ok but the dial in general doesn't look much like those on other 3336s.

Here's one from 1963:

And one from a couple of years earlier with decimal scale:

The handset on your watch doesn't look period correct compared to the dauphine hands on those either. The impression is of more simplicity, reminiscent of these watches from a couple of decades earlier:

Best guess would be that the dial had some problems, perhaps because of its naval life, and has been refinished. Maybe they had an earlier model to reference from, something along the lines of: