Thanks mamagrande, your reply gives me hope. My husband says the shelves will be at least 20" deep, so I've been folding a few pieces to fit that space. We'll be going to our new home in a couple of weeks, (I'm hoping it will be permanent, if not it'll just be another visit) so I"ll take what I've folded from here and begin the new method. I like your idea. What would we do without bins! I'll have this one full before we leave!
I'm glad your new space is working for you. It sounds wonderful to have a place for your fabric.