In your place, I would search the forum to find recommendations for watch repair / watchmakers for vintage Omega in the US. These days, it's harder to find someone local, but there is nothing difficult about shipping this watch domestically. You can just put it in a small priority mail box, and send it fully insured. Several people are often mentioned (e.g. Morehouse, Zimmerman, Mackrain).
They just try it. They will most likely outsource the work to a 3rd party and make USD 1k in the process
The condition of that case is really unusual, especially for a dressy watch, it's so beat up and worn, but not polished. It's as if it was left in a junk drawer. It will be interesting to see if Omega Addict can do a professional refinish.
I'm betting he can.
Omega Watch Service - 1956 Constellation Chronometer
service 300, mainspring 25, remove rust 30, screw extraction 10, 1 x screw 5, 2 x winding gears 30, setting spring 39, crown 50, stem 22, case detail 25, crystal 37, band 39
$632
