Ogre storage problem

I have an Ogre storage problem.

I've been storing my giant Ogre box upright, but everything keeps spilling out of the bottom trays into a giant mess.

Laying it flat "works" except it takes up too much space. I don't really have a good place to lay it flat and out of the way.

Anyone have a good solution for storing the massive Ogre box upright without everything just spilling? Do I need to get a bunch of ziplock bags, or jury rig some kind of lid for the trays?

In theory the maps do that . . . but I can vouch for the fact that, in fact, they do. What do you guys with the Kickstarter Deluxe Ogre extravaganza do for storage?