Thanks for the suggestions QuiltE, I worked with engineers and public meeting projects and sign shops and stuff for years and had access to leftovers but now I'm a decade or two out of date. Print shops are another cool place to get things like large sheets of paper suitable for tracing. Way back when before we had quilt tools, I bought a large plastic triangle at a drafting shop to help square my finished quilt edges. Still have it, fluorescent orange and no markings but no less a right angle.
My husband works for a box making plant and I also have access to really nice cardboard that is heavy stock and large enough -- again, it is scrap for them (and that's one of the things hubby does, is the inventory and scrap management). But I just like that bright white sometimes, and can envision it with fancy duct tape edges whether it needs it or not! Fleece is a good idea, I know that if what you want is something that sticks, you really have to take it on a piece by piece (or at least line by line) basis. Mostly I just want something that is wide enough but that I can fold over and put behind a door easily.
If I can get motivated and clean out the closet in my sewing room then my fabric can go in there. Currently it holds long term storage items like sleeping bags, but I haven't slept on the ground in about 10 years and if it happens again that means things got so bad then I have more to worry about than getting rid of some sleeping bags now! Right now the fabric is in boxes on rolling metal racks in front of the closet. But eventually I will have a nice double slider closet door open to me. "All" it requires is a bit more effort than I apparently possess. It is on the list though.