I started off going to the local HF to look over their catalog of portable bin boxes, and I found two styles I could live with for a quick prototype. I noticed that 2 of the smaller medium boxes were just a bit taller than one of their large boxes.
With a car full of bin boxes, I took 2 small ones and one large one into IKEA with me to stuff and prod them into all the shelving systems they had to offer until I found a good balance of cheap and efficient.
It wasn't until I got to the kids section that I tried stuffing these into the TROFAST shelves, and noticed that they would not stay on the plastic rails as I had hoped, the bins were just a little short, however I noticed another one was equipped with the TROFAST shelves, and I tested the large bin in, and it fit very well, and 2 of the medium bins I could just squish in barely. Good enough, because this means I don't have to engineer anything, I can just stuff it all together and call it a day!