They cut the divider boards so they sat a 1/4" above the top of the deep. This way four 1/4" thick covers could be used on each compartment. Then a regular cover can be placed over the four smaller covers. I think I may do this.
That is what I did we these -> http://forum.beemaster.com/index.php/topic,16515.0.html
What is your mating percentage with the entrances all on the same side?
Why not just use the luan for dividers and as four separate inner covers?