I'm trying to visualize what the end product would look like... Are you going to set it an top of a desk so it's 3' wide x 1' tall x 2-3" deep?
If it were my project, I'd decide what was going into it, then design around that (maybe you've done that already).
Then I'd lay it out; for example, draw out lines to identify "walls" vs voids, shade or mark areas to remove, etc.
If the cubby is something like a grid (voids go all the way through), I'd hog out the majority of them with drill bits. Then clean up the shape with rasps, files, chisels, etc. If voids don't go all the way through, I'd still hog out waste with drill bits, just set some depth control. Cleaning up would be more difficult as the tools would bottom out, but would still be do-able.
Last, I'd go after it with sandpaper, using EVERY sanding assisting device I could possibly force to work!
Routing is great! For production work... after you've designed a set of templates and guides and practiced your set-up, hold down, and technique. For a one-off, it may prove to be more work than time saving, and one slip means redisign time has begun!
If you know anyone with a shop-bot or some such CNC-type router set up, they might be able to do it, but cost could be high since there's be so much set up time involved.
If your design calls for larger areas to be hollowed out, they make chainsaw wheels for disc grinders now, as well as carbide burrs of various coarseness. They're specifically designed for carving out bowls, chair seats, etc. Definitely time saving, and fun! (Assuming you like to watch chips & dust fly!)
Dremel-type tool for finer work in tight spaces.
Basically, anything that removes wood could &should be employed! It sounds more like a sculpting project than a woodwork/assembly project; set mind accordingly and have at it!
