The tow truck beds I always thought looked best on the AD trucks were the ones with flat sides and round tube along the edges and those round fenders that stick out the sides.
The size of the truck probably means it will take some big curves, so something similar to your drawing should be about right. I think if it were me I'd keep the whole thing lower than the windows on the truck. Not only is that practical in that it improves visibility, but also I think it will look better.
I'd spend some time looking at the modern beds made for exactly what you describe to see if you can borrow some storage ideas from the pros.
Those are my thoughts...
