Welcome to RabbitTalk, HoppyMeal! :welcomewagon: (love your name... we like making Sloppy Hoppies here!)
We have similar weather. It's been in the low- to mid-90s lately, with a heat index over 100* like you.
My rabbitry is made of spaced slats on three sides for air flow, and two layers of wire for the front. It is under two trees, but I have learned that for a while before and after the summer solstice, the shade is not as much over the rabbitry. I plan to take care of that with more trees.
I do have a fan in one end of the rabbitry that we turn on in the late morning when it is getting really hot.
That's it for what I do.
Lots of members do use ice bottles, or they freeze large floor tiles, some have misting systems or swamp coolers (which are less effective in humid climates, and would raise the humidity in the rabbitry). Misting burlap is done by some, and would fall into the same category as the misting systems and swamp coolers. You be the judge based on your humidity. Recently, I haven't even been able to fully dry clothes on my clothesline, because it's been too humid.
One member, Paradox, has a very innovative system inspired by rabbitry design in tropical climates. Instead of a cage with a short clay tunnel that leads into a clay pot that is buried up to the lid, Paradox has PVC tunnels that lead to ice chests or even heavy duty totes, that are buried in a raised garden bed, and covered with a hinged roof. Paradox puts regular, personal-size frozen water bottles in each ice chest/tote, to help cool the environment in there. You would have condensation to deal with, if the rabbits didn't lick it up.