perhaps the most sensible course of action is to service it independently with no polishing. Don’t replace anything except gaskets and crystal. Then you can wear the watch and decide how far to go later.
Be very clear with the watchmaker - no polishing and no replacement except movement parts, crystal and gaskets.
these are super rare, and of the very few originally sold, I suspect many were melted.
The last one sold at auction for $52,000 in 2015
https://www.phillips.com/detail/omega/CH080515/243
You might consider polishing it - but there are two sides to this course of action, and many here will have strong opinions on either side. I personally don’t like beaten up gold watches, and others will prefer the unpolished look.
The watch would look much better with the original finish, and so I would consider returning to the factory (not an independent) - working on a gold case is something I would want the factory to do - and yes I would do the case if it were mine. The original finish is done on a lapping machine and not many people have the machine, less have the skills, and even fewer have lots of experience with gold.
Sending it to the factory is giving it a “blessing” as opposed to an independent watchmaker, who however good, risks “cursing” it by polishing it, in terms of future value. However good he is.
Others will demand leaving the case alone and I accept that it may be better to leave it - this is something you have to decide as the owner.
if you are going to sell it, then definitely don’t touch it - every bit of work you do eliminates a group of buyers, so in order to appeal to everyone, leave as is. The pool of potential buyers for this is small enough as it is - let the winner decide what to do. Don’t eliminate the ‘unpolished’ brigade by polishing.
If sending direct to Omega, before you do ask if they have original spec pushers and crown.
I suspect this is a rare enough watch that the right people in omega will pay attention and not mess it up.