The first task was to frame in the rest of the bed. It needed some outside framing on the back wall to hold the supports, then the top portion can slide out from couch to bed.
We will probably add a leg or some other support under the front, as 1/4" of plywood just doesn't seem like enough for nearly 400lbs of us.
The next task was to prop up the rear ceiling that seems to have sagged a bit after being installed. Using cheap home depot pine was probably a mistake here. First, we built a support and pushed the ceiling up as high as we could.
Then we glued an already bowed rafter next to the bent one. The next day, after removing the support the ceiling ended up just a little high, leaving some room for more sag down to flat.
Finally, to try and reduce any more wood damage from the blistering sun, we insulated as much of the sides and roof as possible using rigid foam insulation material.
With only two sides and half the roof, the temperature inside is already at least 10 degrees cooler...very tolerable to sit and relax and think about the electrical work we need to do next.