
Here are two different takes on knife storage by Supergrau, a furniture and housewares company with a Made in Germany product lineup. The Saddle (above) is a magnetic, leather-covered "roof" that provides a place to tuck a cutting board while keeping your knives stuck to the outside. The leather will get scratched up over time, but that's intended to add to the aesthetic.

The Wrench is a nice twist on the standard knife block, replacing those dull slots with perfect geometry. Concentric, hexagonal-cross-section pieces of wood, nested and fixed in place by compressing an O-ring between each section, can store up to 12 knives in a variety of widths (though the cleaver will probably need to ride the Saddle).

Comments
For the cleaver just add a magnet to one face of the Wrench, thus combining the concepts.
I wouldn't put a big, heavy, unstable chopping board under something with knives on it....