I keep wondering about the Art Bin - I have see it on YouTube. The biggest one I can find locally isn't deep enough to store them with the lid on, and if they do fit isn't it really heavy?
Right now I am using a Recollections storage unit. It is similar to the Jet Max style cubes they sell but only half as deep. Inside are 9 compartments. I will have to measure dimensions but each compartment fits 36 Spectrum Noir markers with almost enough room for another row. They are square so it is 6 rows of six markers. Copics would definitely fit another row vertically and possibly even more.
Like all of those products you have to assemble yourself and the interior shelves don't screw in but seem sturdy enough. Regular price $39.99 but they have 40% off sales all the time (like this week). I would have done the foam board but I feel like I would totally mess that up!