I've been using these comic book boards for years. I use them to store 2 yards or less. Any bigger piece than that gets ruler folded and stacked flat.
For the comic book boards, just take your fabric and fold it with selvedges together, as it is on a big bolt. Then fold again, lengthwise. That should leave a width that fits well on the boards. Then wind the fabric around and secure.
I can't stand digging to see what I have, so I store these like books on a bookshelf, only one deep.