I don't have any experience with a system like you describe, but I doubt it will work. Your issue is the big mass of hot air inside the greenhouse. Cooling the roof won't efficiently cool the air. Also what are you going to do with all the hot water you generate? You can't recycle it to the roof, it'll be too hot. I think you have to deal with moving and cooling the air and that means fans and other air handling equipment.
Do you have shade cloth up?
