Yes, IMO you are missing something, there's a reason that experienced collectors don't buy watches the way you're proposing to do it. There is little upside to buying a mediocre, common vintage Omega for 3x its value from an unknown quantity who claims it is serviced. I know that you want to talk yourself into it because it's the easy path, but you should go into it with your eyes open. Another elephant in the room is that out of all the possible references you could have chosen, the watches you have posted are either utilitarian or unappealing, IMO. Taking more time to develop your eye could help you choose an example that will suit you better in the long run.
The service/warranty are only as good as the seller. You may think that they are reputable because they have a fancy website, but that's a beginner's mindset. Many of these internet sellers lie about a service (or have a half-hearted service performed) and offer a warranty gambling that the watch will survive a year, which it usually does. If the watch stops working, they may send it back to the watchmaker and ask them to do the minimum to get it working again. More experienced collectors usually prefer to have the watch serviced by a watchmaker of their choice, who will do a thorough job and provide a warranty that means something.
In your place, I would take more time to understand the nuances of vintage Omega, which will probably result in an evolution of your taste, and an upgrade from the references that you have selected. You might also join a watch enthusiast group locally, so that you can handle and experience some vintage watches in person. Then you can wait patiently to buy a good example from a collector or auction (in the UK or elsewhere), and have it serviced by a recommended independent watchmaker. If you don't have the patience and just want to pay an extra thousand to get a watch immediately, then so be it. But you should at least consider buying from a seller in the UK who gets good firsthand feedback from forum members, and I have read a number of recommendations in previous threads.