How about those really big tna bags, are those allowed? They're big so they'll fit everything you need. Puma, nike and lululemon have them too if you don't like tna.
http://i10.ebayimg.com/06/i/001/05/50/772a_1.JPG
Or how about this hollister one?
http://www.hollisterco.ca/webapp/wcs/stores/servlet/ProductDisplay?storeId=11308&catalogId=10201&productId=449637&langId=-1&categoryId=12624&parentCategoryId=12552&colorSequence=02
They have other ones too. lol but this is my fave.
Umm these aren't backpacks so they might work (especially the hollister one cuz it's smaller), but i dunno. If these aren't allowed either just put everything you don't need in your locker and just take the binders you need. Or you could have all your subjects for the morning in one binder and use dividors.