Thanks for the input everyone! I ended up not using a solid piece at all (slats only). The direct quote from the boss (who wasn't 100% on board before the test) was that it was "surprisingly comfortable". And that was just with Thermarests (they are the extra thick Camprest, however). Ultimately, we will get/make a foam cushion top.
Please don't mock my workmanship as I'm a hack at woodworking and I threw this together faster than I wanted to. The supporting frame is all made from 5/4 x 6 (true 1" x 5.5") deck boards that I had lying around. The slats are standard 1x3. Back section lifts off and the main section is hinged to access storage.
It has its issues, and this was only one night, but I think it's going to be a good starting point. This trip had to seat 3 and sleep 2 hence the middle row seat still in place. I need the 3rd row available for use for the next year, so it's still in there, too. After that, it will come out and we'll lower the bed for more headroom.