Omega service is recommended every 3-5 years for their watches. Winders are ok for Omega watches, so its probably not the cause of your problem, more likely just needs a service. Your "misconception" that the watch can go long periods of time without a service is a bit questionable, and more expensive does not always mean it will last longer, just that it costs more.
$500 is not the price that Omega charges for a full service, so I don't know who quoted you that. I beleive the cost is under $300 that includes replacing damaged/worn parts. If there is a local watchmaker that is reliable, they can probably service it for less than that.
Indeed, your Seiko has functioned well beyond its expectancy, but with Seiko, the charge to service it will also probably be around $300(if you can find someone to do it), to which you promptly throw it in the trash and get a new one. Not likely to do that with the Omega, so get it serviced. By the way, the UN you have probably has the same base movement that the Omega has (ETA 2892-a2). So you should have that one serviced every 5 years or so also, at a cost of probably $600-700.
Sorry for your troubles, but owing a mechanical timepiece does come with risks of failure and costs of maintenance. As I have said before, I equate it to owning a car--sure you can go 25,000 miles without an oil change, but don't "expect" it to not have problems because of it.
