I am about to enter the realm of closet shelves and stashes. I don't know that I have an answer but Closet Maid(?) makes a very easy system for putting up shelves. One long bar across the back of the closet from it hangs the rack (you can screw these into the wall too) that you put the shelf supports on (like in a pantry) then the wire shelves are locked into place. The long bar gets screwed into a stud.
I have a question though.... doesn't having your fabric in tubs cause then to mildew (smells that way) somewhat? In the deep south I think it works because it is wetter outside the tub than inside but what about other places?