I'm sorry you are having to go through a move at this time. We've lived in our house for 45 years & I can't even begin to think of how we would move. DH is a hoarder & never throws anything away....not even bad stuff that is no good.
But if I were moving I would get rid of all my scraps/small pieces & only keep larger pieces of fabric...1/2 yard or more. Then, if I still had too much I would sort between what pieces really make me happy & which ones don't & get rid of those that don't. Now for me, if I downsized like that I would only have a handful of fabric because I generally don't buy in yardage but just what I need for a particular project. But if I had tons of stash that is how I would do it. I bet a local quilt guild would like some of your fabrics for charity projects. Good luck.