I want to trellis a melon or squash over a very hot wall in my AZ garden, too hot for most things to grow on. I'd like to grow something that I can use for chicken feed. Considering a melon or squash. Looking at some of the Asian melon or squash. What would produce the most in sheer amounts of food in a very hot environment? I can provide flood irrigation every two weeks with supplemental water in between but less water in between flooding would be preferable.

Would a bitter melon or some sort of pumpkin be good

Or, would something like a climbing green or giant amaranth produce more food?