Franken dial on a genuine 26.5 SOB T2

Hi everyone!!!

I would like to know if anyone is able to give an opinion on this watch.

At first I thought it was a Franken, seeing the dial. I won the auction, hoping for a correct caliber.

I got lucky because the caliber is a 26.5 SOB T2 and the case looks original, as does the case back.
From the photos you can see the movement, which moreover is in good condition considering its age (from the serial 8762229 it should be from 1935).
I had my watchmaker disassemble the dial to find another original one, and here the doubts began. The dial size is 28.9 mm, which is obviously compatible with the caliber.
I had many misgivings about the hour markers, which except for one case (https://www.chrono24.it/omega/1951-...tm#:~:text=,stella applicati color oro giallo) I have NEVER seen star-shaped on an Omega. They are, however, applied, of two different sizes at 3, 9 and 12 o'clock. The small seconds sub-dial appears badly drawn, with unattractive traces of paint.
There is a serial (19367, several revisions signatures (e.g., “Picconcelli” with a handwriting that is clearly traceable to the 1940s-50s, “Filli” with a more modern handwriting, and the dates “1962” and “11 55”) strangely in Italian (the watch is from Japan!) and a logo (“L & Co”) on which I had AI do a variety of research, getting conflicting answers. I was told that the logo could be Lemrich & Cie or Jean Singer & Cie, but their logos appear to be different.

On eBay I found this dial

(https://www.ebay.it/itm/355648671072? _skw=quadrante+omega+29mm&itmmeta=01JVT42P8BPHJ0T5HJA047ES3R&hash=item52ce500d60:g: nqUAAOSwMypmIj04&itmprp=enc%3AAQAKAAAA0FkggFvd1GGDu0w3yXCmi1dFU%2FpOM%2F51efRiFzmRcI4xa04tqz9mqhPnBv1%2F1hP8D0vwEms6xH9Fjgo4LT1k25zLKrIiyIeerNPyRTSGGYXGpObbacnnOnBsaKDK7R4U45tnB%2BJ8Fr94ZAMt9IxKip9Ba9pL7t2Ii6UYhkf41t3vqGyg4ckjjaBMuwqPbaJDjGsddk3nN75ldGhnomx1iQNL%2FroxUsQL9hQ7PQoRl3Z5ao%2FWdISkyfOfK4HYCq6diXVrPUSy9rNodg%2FyosYqXSI%3D%7Ctkp%3ABk9SR8zkisTeZQ) which is claimed to be original and has the same logo as mine, as well as the same caliper clips.

Does anyone know what this logo can be traced back to?

Expecting that the dial may be, in my opinion, a non-philological remake (from the 1960s? 1970s?), and that the position of the Omega logo is really ugly, in your opinion is it worth keeping this dial, which I think is at least constructively original, or should I look for something else? If so, what dials would you suggest for this watch?

Thanks in advance!

I forgot mentioning that another possible dial manufacturer could be Flückiger & Cie. Even though, according to this article (https://www.contatorideltempo.it/casse-longines-in-materiali-preziosi/, you can have it easily translated from Italian with DeepL or similar), the time line should be different to the watch serial (1935).