Thanks everyone for your suggestions. I was so worried that cardboard boxes would discolor the fabric. I envisioned brown lines on the edges where the fabric touched the cardboard.
had thought about packing my fabric in tote (plastic) boxes, but then I would have so many of them laying around after I put my craft room back together. I have wall to wall cabinets with shelves and doors that I keep (store) my fabric in, that I will be taking with me, so I really don't need any totes to keep, for storing fabric in.
I've decided to go ahead and pack my fabric in cardboard boxes, since it will be safe for the fabric and then I can just recycle them once I'm done.
Fingers crossed for a seamless and quick move! Thanks everyone!