I would cut freezer paper to the size of the white blocks in the white and red section and then iron them on the back. Use and old rotary blade and it should go pretty fast. Then I would iron on strips of freezer paper to the big strips of the white. You should be able to fold the quilt up and take it with you. Then after everyone signs it just peel the freezer paper off. I had individual block done and then people signed and I put them together later. Maybe other people would have suggestions of other ways to stabilize it.