Thinking of what you have shared about your new setting, what about an upright file holder, sitting on your shelving in the closet?
On the corner of the cutting table, I have an upright file holder/bin that I put all larger rulers into. It's only about 4" or 5" thick. Then in front of it, I have a smaller letter holder with a couple of dividers that I stand the smaller ones into. My large 16-1/2" and 24" squares just slide on the floor, into a crack between the cutting table and wall.