Has anyone replaced the radiator? It could be clogged or have damaged cooling fins that cause it to not cool efficiently. If you haven't done that, I'd start there. I'd also be interested in knowing if the thermostat is new as well.
As for the A/C, if you have a hot motor you're gonna have hot air. They are pretty much intwined, so no real surprise there.
The idle issue sounds like fuel. I'd check the fuel filter, fuel pump, and also check that the wiring order is correct going to the Ignition Control Module. You may have something crossed up there as one of the shops could have put one wire back wrong. Easy to do if you don't pay attention.
Given the customization with the body kit, this may well be something that @Mod_Man might have some experience with.
No one has mentioned the radiator being an issue or the fuel pump ..that is an idea Ty!