The Birks Ellis lettering was circa the 1930s or so. Birks used to put there name on various watches, including there own brand, which i am
sure you already know. Ellis was a major jewellery firm in Toronto and joined forces with Birks and Ryrie and the three of them were
in business together for a while.
The logo of Birks could be tracked for images I would guess. I not sure when Birks started to put their name on watch dials. But as Francois mentioned, the dial is probably reprinted or touched up. Francois has helped me quite a bit with my research into my Omega.
Ellis logo or lettering may also be researched for what it might have looked like in the 1930s.
Perhaps you could contact someone at the Birks Phillips Square main office for some help in your research. They probably have a record of old catalogues you may look thru.
The OMEGA logo doesn't look right either. It might be hard to find another reference dial to compare to but others in the Omega Forum I am sure may be able to help you. The serial number as you mentioned is in the mid-1930s which is right.
I used to work at Birks Head-office at Phillips Square in Montreal in the 1980s.