From Florida as well, feel your pain. Matter of fact just came back from 8 hour round trip through FL... sweated off good 10 pounds for sure.
I do have a soft top headliner from hotheads, it works. But, i am skeptical of it. Part of me thinks it is as good as it can get with soft top, and another part of me thinks that i can make my own, much better for much cheaper.
However, i do have tan color top, so if i feel like a fried chicken with mine, you are X10 times worse with your black.
Noico, Dynamat or Kilmat will not do jack shit for stopping heat. They will simply absorb the heat, and will be just as hot as your tub. Who ever suggested that nonsense, go ahead and make a video of yourself driving in 100 degree heat with that noise insulator and then give it a touch around transmission/engine area... so that we all could have a good laugh.
You need heat insulator, something with foam or fabric, similar to under the hood liner (but without fiberglass).
Something like original carpet or this https://www.amazon.com/gp/product/B01K9X452Q/?tag=wranglerorg-20
@Steel City 06
has also provided two links to things that look like a good heat insulator.
I do have a Bedrug, it is a carpet made out of foam. It works, but not any better than any other carpet. I also have a thick floor mat on top of it, and my floor is still very warm to touch, even with constant AC blowing there.
One interesting thing that i have noticed is that with carpet, things are not that much better than with bare tub.
I put in that Bedrug carped few month ago, and this is my first summer with it. The only difference im feeling now, compare to are tub, is that there is no longer a very hot surface next to the pedals, but overall there is still just as much heat coming from underneath. Before the carpet, tub used to work as heatsink. Now that heat radiation is blocked by the carpet, but heat is heat, it has to go somewhere! So as a result, now all the heat is radiating under the center console, and center console has become a new heater.
Heat radiation simply transferred from one place to another. If i stick my hand into console crevices, it is an oven in there. And if heat used to concentrate just around firewall - pedals - shifter area, now it has spread all the way to rear leg area. I cant even keep a cup of ice in cup holder without it all melting away before i notice.
My next step is to figure out what to put under the center console, to force that heat go somewhere else. Additionally im gonna purchase more of that insulating mat that i linked above, and somehow try to place it on firewall from under the hood. I know JKs have insulator there, so i wonder if it is sold anywhere.
mentioned, TJ AC is a joke to some extent, it needs some milk! I recently serviced and refreshed my AC components, it is still as good/bad as it was. This 8 hour road trip i took with my friend, she followed me in her Toyota sedan. It felt like a freezer in her car when i hopped in during one of the gas stops.
Weak AC and this retarded amount of heat coming from engine/trans area is a significant factor during the summers.