Oscar
That is the absolute coolest watch and, as Jeff said, an even better story.
I would get the watch serviced--and sealed appropriately-- but I'd leave the dial alone, even if you could find an exact replacement.
It's part of the story of the watch. The flawed dial is what makes it your father's watch, and that's what makes it truly priceless, and more valuable every day.
If something needs to be done to stabilize it from further deterioration, do that, but then wear the watch in good health,
think of your father every time you check the time, and preserve it for your son.
best
Allen