A lot of people store their Copics in the
Double Deep Art Bins, with the grid for marker storage (the linked website has other sizes/options available), or with
the grid that's designed to cover lights (they are available singly in the store so you don't have to buy the 5-pack) cut to fit. I was going to use it for my Spectrum Noir markers, but the barrels of the markers are slightly too fat to fit the grid. You could lay the bin on its side to have the markers horizontal, or put the grid in a box of your choosing... I haven't seen the Blendabilities yet, so I'm not sure if any of these options are a good fit, but maybe they're a jumpstart for an idea