I have the same heat build up problem when towing in rising terrain when the temperatures are above 34C (93.2F). The issue I believe is related to overfuelling (trying to maintain a descent speed under load on a grade) which can be detected by monitoring Exhaust gas temperatures (EGT). Once your EGT goes over 1000F (at outside air temps of 93F or above) you are making more heat than the engine can shed to the environment (whether via the cooling system or airflow) and the heat will slowly build (assuming overfueling continues) and eventually (if not reduced) the engine will be put into limp mode to protect it. Of course the use of AC does add to the heat load but it is unreasonable to think we should have to turn it off in those conditions to gain a small advantage.
I do not think that a fan clutch is the issue in your case because it would probably overheat without a towing load in rising terrain. I have tested my fan clutch and it works as it is supposed to.
I found, through the use of my gauges, that the optimal towing solution in hot weather is to hold the KJ in 4th gear with the TC locked up at about 1900 -2000 RPM, this has a couple of primary effects: first it changes the gearing thus you stop trying to hold overdrive 5th in rising terrain (which will mean overfuelling) by pushing ever more on the throttle, and it reduces transmission heat build up; secondly, EGT drops immeadiately to a more reasonable level like about 900F or less which means that less heat is being dealt with by the cooling system; thirdly, your fuel economy will be as good if not better than normal cruise on flat terrain (while towing) because your are in the rpm range where the VM engine is optimised for fuel economy (2000rpm). Have a look at this chart provided by VM:

Finally, IMHO all KJ CRDs should have a good aftermarket auxiliary transmission cooler to shed the heat generated there, and a transmission temperature gauge is a necessity. So in a nutshell, performance is optimised and temperatures controlled by managing the KJ operations to achieve the lowest possible temperatures on your: EGT, engine coolant temperature, and transmission (regardless of speed and terrain).
As a note, diesel Chips and Tunes modify fueling operations to produce additional power and this may mean that overfueling is used at some points compared to stock configuration (which can mean more heat being generated). Of course GDE's Tune does other things as well, like remap boost etc. I run the GDE Eco tune.