I was looking at a crate just now, and realized it looks an awful lot like a really big drawer.... How about we build a "storage unit" out of a bunch of planks (12? 15?) to make a 1x2 stationary furniture object, which would behave much like the cart interface. It could show the crates as filled or empty drawer sprites, maybe six of then stacked top to bottom or whatever. You'd get more condensed/rational storage options than a cabinet, but at the cost of having to pull the drawers out individually to access them.
It would have to take more than four drawers to make it in any way desirable over a standard cupboard. 6 drawers x 15 /drawer = 90 items, vs 8 x 8 = 64 items? Maybe it isn't worth it, but who knows. I'd do a little extra schlepping for a 50% increase in storage space.