Request Identification Assistance

Hello...Can someone please help me identify this watch?

It was originally my grandfathers, passed down to my father and now to me. Probably purchased in the New York City area. I have done multiple Google image searches and haven’t found anything exactly like it. Many look quite similar but the two major differences I see are mine has Roman numerals at 12, 3, 6 and 9 while the others have Arabic numerals at those locations and mine has the name “Omega” on a little raised bar on the watch face while others have the name printed directly on the watch face.

It is currently being refurbished (not sure that's the correct term...taken completely apart, cleaned and polished where appropriate, reassembled) by certified master watchmaker, Kent Mikolite, here in Chicago. When I get it back from him I can post additional pictures.

What I do know...18K gold case, serial number #10870796 (one search said 1944, another said 1947?), bumper automatic movement, case diameter about 36mm.

Thank you in advance for any and all your help.
Gordon

What else is on the inside back? Maybe a 4 digit number. xxxx- x. That’s a reference number. You can search on the model with that number

omega xxxx-x

Never had one, but called a Plank dial?

Edit. This model doesn't have a 4 digit and the long number is a reference number? Never looked that type up

Perhaps you could ask the watch doctor nicely if he could take some happy snaps of inside the case back whilst it's off?

I saw this model a few years ago. They look great. Some pictures for you. This is not mine