A comment on dimensions. Regular twin mattresses are 38" wide and doubles are 54" wide. It looks like the widths of the 2 sections in the pictures are about 30" and 30". Beds for semi trucks are commonly 30" wide, so you can get mattresses and sheets in that size.
In my GMC van, I have a regular 8" thick foam twin-size mattress across the back, 38"x74". The width just above the wheel wheels is a perfect match, at 74-76". Unfortunately in the Savana van, there is a heavy metal strut that comes down to the top of the wheel well which causes some interference problems, that you don't have, and makes a double width bed more of a problem for me.
The front of your wheel wells will probably cause some interference problem, but you can cantilever the front edge of the bed pullout if the upper horizontal piece is strong, ie 2x4.
Assuming you are building a convertible couch-bed, then you want to pay attention to how "deep" the horizontal part is when in couch mode. Most couches are way too deep between the front edge and upright cushions in the back. Most chair seats are about 16"-19" deep while couches are much more. So assuming you do the 30",30" build, if you use an 8" cushion for the back support, then the depth of the couch will be 30"-8" = 22", not too bad.
I do about 90% of my storage under my bed, so you will want to consider what sort of containers you will want to use before finalizing your design. My containers slide right out, but if the bottom board is too thick on your design, it will interfere with pulling out the storage containers. What fun.