How many chickens were you planning for?
I'm thinking you can keep your cinder block building and the cement floored portion completely separate from the chickens. I know our cinder block buildings got extremely hot in CO and the horse barns that I visited in Florida were often so hot it was almost instant "pass out" for me (the ones in Florida had a lot of ventilation (usually completely open from 6' or 8' to rafters/roof) and also very large barn fans, but)... That's hot for chickens. I'm not sure you'd have enough ventilation in the enclosed cinder block portion - w/ no windows on either side. I would have to look at your pictures again.
I would read this article in chicken coops -
Hot weather coops
Here is another one - but it started from scratch -
New Chicken Coop - a work in progress
Carport to chicken coop/run -
in Florida
I was looking for a couple of other carport type builds, know we have them on BYC, just not finding them...
I'd frame it out in hardware cloth, just like you are already discussing. HC to keep your birds out of the rafters and in the area you are setting up the coop. Not really sure you'd even need to put a solid wall on the outside - when there are 2 sides fully enclosed.
Lots of different styles of nest boxes that can be set up in the partially enclosed area, along with your roost. Many different ways to do the nest boxes - could be free standing in the open area; built into a "wall" (other then the nest boxes, wall could all be HC) along the cement floor side so that you don't have to go into the coop area, etc. Storing feed in the cement block storage building, plus any other supplies would be ideal.
I'd love to have that as a set up to begin with!! What a score and so many different ways it can be set up.