The reason for the lack of SWISS MADE on the dial is that the dial was totally repainted very poorly at some point in the past, presumably because it was damaged. Please look more critically at the dial (comparing to the photo in the link you posted) and you will see that the printing is sloppy and the fonts are completely wrong. It did not come that way from the factory. We have looked at thousands of dials so it immediately jumps out at us.
The watch was also re-cased in a non-Omega case, as noted above. Also, the hands are not original. Basically, it is put together from mismatched parts. At what point all of this happened, I can't say. Many things can happen over 40+ years.
Your idea of having the movement repaired by an independent watchmaker is a good one.
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