One Longines case reference that seems to be what you are looking for is
Ref. 7035. However, it seems that these watches do not have the word(s) "Swiss" or "Swiss Made" on the dial. That makes it difficult to discern originality of the dials.
Here are threads on our forum that talk about some of the watches to which you refer:
https://omegaforums.net/threads/1950s-longines-calatrava.36802/
https://omegaforums.net/threads/lady-luck-delivers-an-early-longines-chronometre.11157/
However, there is a lot of debate and disagreement over the originality of the dials on the first post.
The second post shows a fantastic 36mm Longines Chronometer owned by a member here. That one also does not have "Swiss" at the bottom of the dial, but it looks fully original to me.
I'm not sure how to tell if dials are original on these references.
gatorcpa