I voted for metal roof because I live where its hot and humid also, with the sides open there's no extra heat from roof. my girls get plenty of light even though coop is nestled in among many trees. I started with poly carb roof and after a couple years it was cracked in multiple places from branches and acorns dropping on it. It did become brittle and fall apart also, lots of leaks. Hate the idea of no roof at all, the chickens seeing the predators looking down at them would cause all kinds of stress in the flock! You could probably plant in the run if you protected the plants with hardware cloth around base and up a bit so the chickens couldn't scratch up roots or eat so much of plant that it can't survive.