I think your correct in laminating some of the stringers to get the proper shape and keep it strong. I'm also thinking that for weight saving, the bed might just be a canoe seat style webbing to throw a sleeping bag on, like a relatively flat hammock that would roll up and stow in the cab over during the day. Here is a folding boat identical to one that I made, that I could use as a shape starting point. I still have the forms I used for laminating the bows. The bow is abrupt enough to be a good starting point. More laminations would make it a strong platform for attaching the roof frames. Unlike the stern of this boat, I would built straight out the back to allow for a rear door.
I'm glad you addressed the cloth choice as I wasn't sure what would be best. Being as this isn't a boat, constantly sitting in water, I don't mind having a few seams as long as they allow for runoff.