Hacker Help: Containers for Markor

Materials: Markor: horizontal piece with 5 across, 2 up/down square openings

Description:
I bought the Markor horizontal bookcase (with 10 square openings in a 2×5 formation) a couple years ago, but I never found good containers for it. The squares measure: 13 1/8 high x 13 1/8 wide x 12 5/8 deep (although we could go a little deeper if they hang out the back a little, but I would prefer a good fit).

Anyone done an easy container hack for this? Please share what you’ve done? Or even if you just have a good idea that you have not done, but think will work. I’m having a total mental block on this and would appreciate the help. Thank you!

P.S. Sorry, I cannot get a good picture because it is in a tight hallway space.

~ Elizabeth, US