Advice on heirloom Omega

I'm interested in fixing up my father's Seamaster. He has been the only owner since purchase, serial number points to 1969 manufacture. It has a caliber 563 movement and keeps time but is well overdue for a service.

Based on researching the reference here and around the net, I identified some issues:
-Crown is not original, I would like to get an original crown
-Was re-dialed at some point. Typefaces on 'Omega' and 'Automatic' are wrong and missing 'swiss made'. The applied indices look good.
-Case is pretty beat up, though I'd like to keep it in that condition if possible.

I'm more interested in preservation over collectibility; given that, I was thinking of keeping the original dial and re-dialing instead of trying to find a replacement. My questions:

-What are the pros and cons of having Omega do the work vs a respected 3rd party watchmaker? And the cost differential?
-Would the dial need a full overhaul or could I just get the text re-printed?
-What should I consider doing re: service of the gold filled case? Is it best to leave as-is?

It looks like a watchmaker bent two of the lugs, which makes sense because this case had a weird 17.5mm lug width. I think I'll keep it like that as it would be hell to find a strap in the original size. Would Omega even be willing to touch the case? this reference was one of the American cased references.

Sorry, but that lug width is not "weird". That's a US-production watch, and as such the straps were specified in fractions of an inch. That case required a strap of 11/16", which is 17.25mm.

Most modern straps labeled 17mm are for those vintage US watches.

International collection watches weren't always metric either, I have a CK2930 that is also 11/16".

Good to know, not sure why it was done then. I'll have to buy a 17mm and make sure it fits.

I'd measure first. By the looks of it, 17mm is not likely to fit.

I don't have calipers but looks like 17 even. It was on an old 70s or 80s bracelet when I got it, which I already tossed.

Good enough. You can also find NOS 11/16" straps on eBay if you want one of those.

Just closing the loop here-

I decided to send to Omega and after ~10 months it came back looking and feeling as good as new. Thanks everyone for the advice, and grateful Omega provides this service.

Looks brilliant, enjoy it.

Looks great. The most important thing is that you are happy with the results. I have a 56's Omega Constellation that belonged o my father, and I love the feeling every time I wear it. Congratulations.

Wear it in health.