I have built the bed box. You can see the pictures here:
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The box is 20-inches wide out-to-out. The bed is 24-inched wide.
The front space is accessible only from the top. The rear space could be accessed from the open end or the top. But, accidentally it looks like a plastic container can also fit right in.
The drawings are good but I had to make a few modifications as I started cutting the boards. My neighbor used his router and rounded all the edges for me (thanks, neighbor). The design can be improved, and the box can be made lighter by removing material from areas that are not needed.
Even though the edges are rounded up I still want to adhere a carpet-like strip to the bottom where the plywood interfaces the carpet inside the car. I also would like to cover the sides of this box with automotive grade carpeting/liner of some sorts. I have not found a good source for that yet.
For the two bulkheads, it turned out because the routing slot was made too big, that I needed to use right angle brackets to attach them to the sides. This means the design could have been much simpler and routing could have been eliminated from process - just straight cuts. But if routing is done properly, and the bulkheads could fit right, the steel brackets would not be needed; the brackets are difficult to screw in because of their size and position, but I am sure a good way can be found.
If and when I build another one of these I intend to design it so that the box can be used inside a tent as well. For that a pair of feet at the narrower part of the frame would be needed.
If you have any comment or suggestion I am all ears.