A friend donated some torn jeans to the cause. I cut slits, cable tied the crotch to bring the legs into alignment, and hot glued the bottom of the 'pockets'. Pictured here filled with shoes and socks, but will probably end up storing other things and filling the extra pockets.
I also got the mini projector working in Linux, but the dumb thing doesn't take power when it's displaying something, so from a full battery it will run out 3/4 of the way through a movie! Next step is to open it up and add a proper power source (since it will be fixed in one place a wall wart isn't a disadvantage). Then at least I'll be entertained while I start collecting material for further room hacks.
Finally, I fixed the towel rack with some epoxy and hot glue (the hot glue just to seal around it and hold it in place while the epoxy hardens) - it's a permanent modification to the room but I doubt I'll be in trouble for fixing something so totally broken :P