Those big spools that electric line comes on might work! hate to admit this, but dumpsters at construction sites have pretty good scraps of plywood for free...
We have 2 big tractor tires you could have if you wanted to truck them from Kansas. I wouldn't use big tires on that, though because old tires catch water and mosquitoes breed there. Maybe you don't have stagnant water and mosquitoes in AZ, though?
I like your buttons idea. That smokestack on the drawing could be a place to pour feed in.
If you did the big back tire like a water wheel you could have rotating roosts!
I want to see this if you draw a plan!