What an amazing gift for your son from his grandmother. Love it! I agree with Bearisgray. It would help to see a photo of her quilt.
There are so many Board members that are much more experienced than I that I am sure you will get some great help.
My 2 cents!!! As I have been thinking about your dilemma, I was thinking that perhaps you could pin it to a large rug or your carpet and try to square it up as much as possible. If you pin it with the wrong side up, you may be able to press it (not iron it) while it is attached to the carpet/rug. You will be able to add starch on the back of your fabrics without residue. It may be a slow process but if you get it fairly flat, then the ties will hold it together and even if there is some wavy parts they will be fine. It sounds like a lovely quilt. I never knew my grandparents so I believe this is wonderful. Good luck with whatever you decide.