Do you have room in your run for a "Summer/Florida" type coop? Wire on all sides and bottom with a solid roof.
I live at 30 degrees latitude ( New Orleans) where the sun and humidity are intense for 6-7 months per year. I have never lost a bird due to heat stress, my girls have access to shade and fresh clean water 24/7, but never ice cubes, frozen treats, or any other heat mitigation ideas that I've read about here
"Fans?,we don't need no stinkin fans."
My flock consists of Buff Orpingtons, Production Reds, and Barred Rocks, none of these are small/lightly feathered breeds. Yes, when it is very hot they will be panting with open mouths in the sun- once they hydrate and get into shade -no problems ( and it's the same with me!)
Good Luck with your hens, I've had chickens for 30+ years and will keep doing what works for me and my gals.
I am not trying to put anybody down, if it works for you great- just saying what works for me...