Are you doing the work yourself or are you paying a mechanic to do the work? If you are paying a mechanic, you might want to find a better mechanic. It makes no sense that you paid all this money, and you know the issue is that your car is overheating when the AC is on, and a mechanic cannot diagnose what the problem is except charging you all this money, over and over again. If the electric fan is faulty, a good mechanic should be able to diagnose this issue. I can sit in park with my AC on, and my Jeep won't overheat. Of course, I don't live in the desert. A mechanic should be able to let the car run in park, turn on the AC, and make sure the fan is coming on, and diagnose any issues.
Also, it is not a good idea to let your Jeep continue to overheat and blow out radiators. You could fry your engine. I would NOT run the AC until the issue is properly repaired. Although now, it seems the issue must be resolved because it is even overheating without the AC on. I really hope that you are working on this Jeep yourself and not paying a mechanic to do it.
Lastly, you might want to run your Vin information to see what your Jeep came with from the factory. There are certain part upgrades that were added if the Jeep came from the factory with AC. If the Jeep didn't come from the factory with AC, then this might explain all the "mickey mouse" parts added to your Jeep like the electric fan. I believe one such part was a heavy duty alternator. It seems the PO knew there was an issue and they tried to solve it with an electric fan, instead of finding out what the real issue was. I think your issue is an inadequate radiator, clogged coolant system, and maybe a faulty compressor clutch. Maybe all the original pulleys aren't there either since the original fan was removed. I would also get rid of the "mickey mouse" electric fan setup, and return it to stock. This shouldn't be a rocket science issue for a good mechanic. I've had issues with my AC, and my mechanic was able to fix it pronto. Luckily, I am the Original Owner so no one Mickey Moused my Jeep. Good Luck.