Here are some photos of the dog platform and some slight modifications to the sleeping platform to add rigidity without the third-row seats.
First, some modifications to the rear platform to add rigidity and to prevent it from sliding when braking.
The straps hold the platform on the child seat anchors. The crosspiece is attached to the folding legs with four locking cotter pins, two on each side. The angle brackets are screwed into the crosspiece.
There's also a vertical leg at the front of the platform that's held in place with three t-nuts and hex-socket bolts (like the legs on the front platform). That way, it can be removed when the third-row seats are installed since there's no room for it and the third-row seats supply the same rigidity as the leg.
You can see the dog platform instead of the second-row seats. Here's a side-view with the bed platform collapsed:
It's all just scrap wood and a $20 rubber-backed rug from Target. The rug is held in place with bolts at each corner and staples across the sides. The dog platform is tied to the sleeping platform by rope and a ratcheting pulley to prevent it from sliding forward in the event of heavy breaking.
Here's how the sleeping platform extends over the dog platform:
There's a hole front and center to allow the front leg of the sleeping platform to slot into place. That way I didn't have to have a different front leg for when we travel with dogs. The platform gives us some storage underneath for their accessories (mostly food and bowls/backpacks) and it gives them a nice flat place to travel that protects their paws from the second-row seat bolts. Needless to say, they loved traveling on it. There was plenty of room to stand, sit, lay, and sleep. It also doubled as a place to store some things while we slept. One dog slept in the front seat, one on the platform with us. There was plenty of space.
We also have a travel water dish that we attach to the legs of the rear platform with bungee cords so they have some water while we travel:
That's the primary reason for the rubber-backed mat. It also protects the particle board (remember, it's built with scrap wood) from wet, muddy paws and sloppy drinkers.
The dog platform, during storage, sits over the platforms. The legs on the dog platform don't fold and are cut to size to make the platform level. There are three short legs on the back of the platform, near the sleeping platform's legs that let it sit over the oddly shaped attachments for the second-row seats.
I still haven't had a chance to get some photos of the platform folded and stored; it's not been out of the van long enough.