I've got a 14 1/2 deep cabinet and I ruler fold most of my stuff (or at least the new stuff ) Since you have a lot of half yard pieces I did a quick experiment. If you use a 3 inch ruler rather than a 6 incher, they end up about 1/2 inch thick, so you can see the fabric and it takes up the same depth as as a regular 6 inch fold. I think that it might work better if you put a piece of cardboardish type stuff on either side of the whole stack since it would probably be a little less stable sideways than a 6 inch stack. I just used an 18 x 3 ruler to try it. Even with it not reaching the selveges or the fold it worked fine.