That's a great idea. Back when things were sturdier, I had a Quakers Oat container I used like that for years. I really like the no creases.
My current solution still gives me creases, but not so bad. Since I piece faster than I quilt, I always have a backlog of tops. But before I put them in the to-be-quilted stack they have their back and their bindings premade. I have access to cardboard and cut a piece something like 18" in one direction, typically slightly narrower like 12-16" the other because each 18" wrap means a yard and you can count easily! Then everything gets folded up and stuck away and I deal with the guilt of unfinished tops. So far, I'm pretty ok being guilty but just about at maximum mea culpa... I do plan on actually quilting this year and next too.