If you look at the ebay list I posted there is one without the Seamaster ! As a soldier back in the day you could buy things like this at special pricing for our folks in uniform and some times the watches had less or more depending on what the soldier was able to spend. Rolex did this as well.Pretty please DON'T refinish the dial! It nearly never works out. Not only does it loose it's character in my opinion, it tanks it's value. Being that this is an heirloom watch I can understand that resale value isn't much of a consideration, but 95% of the time a dial restoration is inadvisable. The crystal for that watch is very likely easily sourced. Those movements are very well made. The are brass movements, plated in copper and beryllium bronze. It was a process unique to Omega and it made those movements stunning to look at. You got a great watch and heirloom there.
FYI - servicing that watch will be pretty straight forward. Those Omega movements are very easy to work on (I've done 1 myself already on an old watch given to me years ago). Parts are pretty available, but as long as it wasn't terribly abused, usually the parts are in good shape and can be re-used, aside of course from the mainspring which should almost always get replaced. Think of that as a consumable item in a mechanical watch.
I'd recommend keeping the dial and hands showing their age and only clean up any surface grime that is easily removed with Rodico, clean up the case and put a new crystal in it with a black leather strap. It will be stunning. I'd bet a basic full service is all that watch would need to be a solid runner. I'm looking at a few vintage Omega's online right now myself, and would love to find a pie pan dialed Omega Constellation to restore.
Regarding the dial itself, it is missing the 'Seamaster' script, and it is missing 'Swiss Made' at the 6 o'clock position. Some of the very early Omega's didn't have 'Swiss Made' on the dials yet, but I haven't run across any verified/documented vintage Seamasters that didn't have that script on the dial somewhere, either just below the Omega symbol, or midway between the hands and the 6 o'clock marker. It might be legit, but it would be in a configuration that I haven't come across yet. This might also just be a redial, although very old. There is an Omega forum with folks who live and breath this stuff, and I'm sure they could authenticate it for you with a few photos if it is of any concern to you.
I know more about the dials and their history than the caseback markings, but I haven't seen one that looks like that before. Not to say it isn't original, it's just something I haven't come across yet.
Odds are that the movement is probably genuine. They were super well made, but mass produced nonetheless. If I can help you in any way feel free to reach out. I can help you get the movement info off of it, source a replacement crystal, or put the watch on my timegrapher to tell you how it is running and let you know of any problems. Just let me know.