You need to get this watch back an authorised dealer for forwarding to Schaffhausen where a restoration can be done. Your thoughts re hands and dial remaining original is one I agree with. Polishing the case though comes with two issues. It's age determines that this would not be pristine condition so how far do you want this polished? lightly or to make as new? Laser welding can fill in the dings and chips and can make the case as new.
Your grandfather worked at Sig, for your info there is an old building outside of Schaffhausen that used to be part of the manufacturing plant of Sig Hammerli complete with heavy security doors, that building is now used for the manufacturing of parts by IWC, specifically case production and polishing. Sometimes it's a very small world!
Be aware that a restoration may take 4+ months and will not be cheap but the masters of Schaffhausen can do wonders and yes I would do it if in your shoes. I did the same for my fathers watch (not IWC) and even managed to find a movement on eBay to help in the restoration for donor parts that were required. Dad's watch is a keeper as far as I am concerned.
Think about what you want done, write it down and put the letter with the watch when you take it in to the Chicago dealership. Please don't get the testament removed although that's not for consideration I suspect. I think it's safe to assume that you would never sell it.