Swimmer asked if I used quarter inch ply for all of it. Yes, but around the inside edge of each door, I reinforced the door with strips of quarter inch ply, so that there is a hollow rectangle that is a half inch thick. I used Titebond III glue for those reinforcements.
And yes, we do store some canned goods (in small boxes) on those shelves -- no problem, even though we travel over rocky dirt roads. The shelves are supported with thin strips of maple that are screwed into the walls. (The photos in the blog post, above, show the supports.) Inside the walls, I installed plastic spiral screw anchors. The walls themselves are just very thin ply sandwiched onto foam -- they have no separate structural integrity. So that is the reason for the anchors.
The closures are magnetic catches. But I also installed locking devices at the top and bottom of each door, to keep everything secure on bumpy roads.
The "locks" are just long drywall screws. I bent them at 90 degrees by putting them in a vice and heating them up with a propane torch, using a pair of pliers to bend each one in the middle. If you don't use a torch, the metal will crystallize and break when you bend it.
I then put a little piece of plastic tubing on the end of each "lock." Finally, I screwed each one into the face frame of my cabinet and screwed it down until it makes contact with the face of the door. To "unlock," turn the screw a quarter turn to the left. Very simple, works great, but not real pretty.