Looks great. You might want to take a look at this thread about watch repair in LA:
https://omegaforums.net/threads/trusted-watchmakers-in-los-angeles.79352/
There are a few in Pasadena proper too, but I haven't used any of them so I can't comment.
Standard advice on this forum is to avoid polishing the case, and not to run the watch before it's serviced. If a watchmaker opens it up for you, you can photograph the movement and the inside of the caseback, which will give you a unique serial number and a reference (model) number. These make dating and comparison easier.
Lots of information on constellations can be found on this forum, but the bible is:
http://omega-constellation-collectors.blogspot.com/Click to expand...