First off - I apologize for taking so long to come back to this! I went through one of those phases where I was spending my free time reading or sewing rather than at my computer, so please know I do appreciate ALL of the replies and suggestions I received!
Secondly: I promise, Grandma *does* want this organized. Her typical request for a birthday/Christmas "present" is that I spend some time with her working on cleaning up the basement. I don't mean to come across as wanting to get it done before she dies (I really, really would like her to stick around for several years more), but frequently her reasoning for giving me fabric from her stash is that I'll inherit it all eventually anyway and she probably won't get around to using all of this.
Third, THANK YOU THANK YOU THANK YOU for all the ideas! We are going to get started tomorrow afternoon! My initial inclination to pull everything out has been talked down and we're going to work on one bit at a time. I still have about 2 months until I move and I'm over there almost every day, so with some luck we'll make a fair amount of progress. I've roped Mom in as well, since she "owes" Grandma a couple days from a few years ago.
I would like to apologize one last time for taking so long to come back to this. All of your advice is being taken to heart - we're just going to start, and fold, and sort! Thank you!