Ok, with your requirements, here are my suggestions.
The wire on the bottom: Put it on top of the bottom frame. If it is on the ground it will make it harder to move and the chickens will still tear up the grass.
Enclose the back 2 or 3 feet. You don't want them sleeping in the nest boxes. Add a roost, higher than the nest boxes.
You can use the corrugated PVC panels for the walls, or they have plastic sign board. It looks like cardboard but it is plastic. I would go to a sign shop and see if they have any mistakes. It is waterproof, bug proof and lightweight.
I would hinge the whole roof for easy access for cleaning. Also put wire under the roof and wall panels.
Add wheels at least on 1 end. An old lawnmower handle makes a great handle to pull it around!
Good luck!