Can Anyone Identify This Vintage Omega?

NEW PICS AND INFO POSTED AT THE BOTTOM OF THE THREAD AS OF AUGUST 21ST.
Reference number and caliber? Just trying to satisfy my own curiosity. Doing my own research, but would welcome the input if someone more knowledgeable beats me to it. I'm thinking maybe an early version of reference 2639 with a 26x caliber? Thanks!

I can't possibly have stumped the experts? Say it ain't so!

And I would open the case and look there IF I had the watch in my possession!

Sorry to disappoint. Doing things in reverse order with due diligence first. Oops. 😀

Somewhat similar, but not an exact match.

Ah, good catch! Making progress.

Two more photos:

So, my “mystery watch,” which I purchased on a whim with little information other than a few bad pics (see the top of the thread), arrived yesterday. Following are some better pics that I took in natural light. The dial has some light damage on the edge near the three o’clock marker that is visible with magnification, but is otherwise in very nice condition. Diamond shaped hour markers that look like rose gold to me, but numerals at 12, 3 and 9. The crown is signed and appears original. The case is beautiful with teardrop shaped lugs and all edges and chamfers nice and sharp. Bonus: a Portuguese customs stamp on the top left lug adds some uniqueness. I polished the crystal, which I think may be aftermarket, with PolyWatch and lightly polished the case by hand. The watch winds up smoothly, sets and runs well, but is running a bit fast. I’ll be sending it out to my watchmaker next week for a movement service, but overall I’m very pleased. Still one problem. The watch has a press in case back that I’m reluctant to remove, so I don’t know the case reference or the caliber (other than it’s a manual wind) and I can’t find an exact match online. Before my watchmaker solves the mystery, do any of our vintage experts want to hazard a guess on what I have here - case reference, year of manufacture, caliber? Thanks all!