It turns out that the box I mentioned earlier is about 6' x 4' x 3.5', which is a bit smaller than I expected. However, I'm thinking that we could do 6' length x 4' depth, and add to the 3.5' height to make it at least 4.5'. I was thinking 4' in the back, 4.5' in the front to make a sloped roof.
That should work.
The raised roof will make for excellent ventilation. Make the roof hang well over the walls to shade them and keep sideways rain out of the vents.