I used Ozz's method after seeing what he did except I pulled out the 4x4 sheet of plywood, cut it down the middle, and put a cabinet handle on each half. I just lift out or slide back whichever part I want access to. Ozz gave me the leftover part of that black 3-sided box you see.
Normally the upper level is loaded with the more frequently accessed items with seasonal clothing in the lower area.
If I recall, there were only 2 screws holding the plywood in place once I relocated the safe.
I would think you could easily fashion doors on the vertical panels under the bed for quick access to small items.