I use the same hammock you have. Found a battery powered fan that hangs form the internal overhead line that keeps the netting off your face. Makes 85*+ nights with 95% humidity very doable. It will kill a lithium AA battery in a night if it was left on all night. But even when really warm out I find that I tend to turn it off sometime during the night. Once you stop moving and get comfortable your body temperature drops and it's much easier to keep cool. It's that you are hot when you climb in the hammock then because your hot and uncomfortable you keep moving around and that just keeps the body temp up. As you know moving in a hammock isn't like rolling over on a bed. Its a full body workout to reposition.
So keep an eye out for those little fans in stores. Touristy places near the beach should have something that will work. I like these little guys
But mainly just look for one that when hanging it can be angled to blow on you. These also are very handy in getting wet wood to catch fire. Screw blowing on a fire.