When we moved the last time--4 years ago, I realized how much fabric I actually have. I used cardboard boxes and had no problem. Keeping them to a manageable weight/size ratio is very important. Since you do not know how long it will be, before your sewing room is unpacked, I would make up a few smaller project kits and keep them available to work on when time permits.
Using fabric for packing material is a great idea. I used towels and other linens--never thought of my fabric.