I have been doing the flip. Open the box. Flip it over, suing your hand to keep everything from spilling out. REmove the bottom of the box, and sort out the maps and components that are now on the table.
I did it this way so I could use some standard 100 card sleeve boxes and make them fit (like the cheap plastic UltraPro). Just remove the bottom insert and put the boards on the bottom and everything else on top.