Echoing the other posters here in saying that a service would be a good idea. Seems like you have a lot of memories with this watch and want to keep it running in the long term. A nice trip to the spa would be a great idea. Think about it like buying a used car. The guy you bought it from says he is sure he had the oil changed last year but doesn't have the receipt. Its a good idea to have it in for some preventative maintenance and start the timer on the next service. A ounce of prevention, a pound of cure, and a dozen other proverbs I am sure apply.
Local watchmaker is a good idea they tend to be more sympathetic to vintage pieces. If it went off to Omega they would likely polish out all those dings your dad put into over the years which would be a shame. Not to mention possibly swapping hands ect..
Mostly just stopping by to say that I think you have a beautiful watch there. I am thinking about adding a similar looking midcentury, manual wind, two register chrono to the collection soon. I'll be luck if I can snag one as sweet looking as the beauty you got there. Good luck! I hope you can make some beautiful memories of your own with that watch on your wrist!