I will hose the roof, cold water on it is a big help, unless it's just too humid for the water to evaporate.
And adding a predator proof run, however small, helps too. Then your chicken doors can all be open 24/7.
And hardware cloth covered windows in those big doors!
Mary
Definitely more ventilation needed. And shade in summer. Trees, shrubs, something. Insulating the ceiling helps with summer sun too.
Chickens also like cold watermellon, ice in their waterers, anything like that.
How about an awning, or a tarp or some roofed shade structure? A temporary fix...