Vintage Omega Watch Servicing Advice

Having gone both ways on vintage watches (Both through Omega and through private):

IF you go through Omega, they are going to replace a lot of parts, AND refinish everything. What you'll end up with is a watch that LOOKS as close as possible to 'just came out of the case'. The problem with that is you'll end up getting a watch that looks fantastic, but is historically not very accurate, and likely at a reduced 'value'. That said, the cost here is likely fixed: Omega will replace a lot of the stuff with no additional cost to you (that is, you don't pay for parts).

A private watchmaker is going to be tougher to find a GOOD one, but as others have said, someone can give you a good recommendation here I'm sure. Also, they might end up being mildly more expensive (as they likely are going to charge you for replacement parts). However, the watch you'll get in the end will be more 'original' and honest.

IF you're going to do the former, I would expect "wear it until it stops" is acceptable, since you'll not be paying for the worn out parts. IF you're going to do the latter, I'd suggest sticking to a fairly standard servicing schedule, as you'll likely be on the hook for replacement parts.

IF it were me in your case: The 168.005 (LOOKS like it is a pie pan Constellation? best I can tell from research) is an absurdly awesome and classic looking watch with a ton of value from its originality. Omega service is going to ruin that, and ruin the charm. Have folks here help you find a great local watchmaker who can do a sympathetic servicing with minimal polishing.

I haven't used a watchmaker for some years so I can't recommend anybody.
However, I'd suggest a Google search and then check the reviews.

A couple that spring to mind are

Rory MacDonald

Michael Presser - https://www.precisiontiming.com.au/about/

I don't think you need to be in a rush to find a watchmaker if you are certain it was properly serviced in 2018. Take your time, network with other local collectors, and gather some first-hand recommendations.