I’d say that was a very successful transformation! The redial, crown and new strap look great, and I’m sure is a source of pride on your wrist. A nice reminder of your father and grandfather - wear it in good health.
The case number is a serial one, and it matches the movement's one (same period, mid 40's). So I do not see anything wrong here.
The dial looks good from here, but a closer pic of the logo and text would help.
By the way, the holding screws are not original and do not have the correct size. I would try to change that. But they are not easy to find - at least for an amateur, I do not know if they are still produced by Omega.