Just a few questions to determine your best storage method.
First, are you using the available shelf space to full potential? Is there empty space above the fabric boards? Can you move the current shelves? How deep are the current shelves? Do you want to ruler fold or actually roll the fabrics into rolls?
I ruler fold on a 6 1/2 inch ruler and then fold in half. Fabric pieces are approx 11 inches deep and stacked on a 16 inch wire shelf in the closet.
Can you post a picture of the current space? Perhaps we can help you with more suggestions.