Your distance and rise equals a 4% grade on average. That in itself is moderately steep over that distance. If it's 100 degrees outside you will get some transmission warming but 6,000 lbs is not terribly heavy. I tow 13,000 lbs up the Eisenhower Tunnel on I-70 and on hot days I can't make it (+95 degrees. ) Some times engine temps get me, sometime transmission temps. Depends how slow I have to go. At that weight if something slows me down I can't regain speed because rise is to steep on this stretch of highway. I have a modified transmission but my stock Cummins is weak for 13,000 lbs in my opinion. I would be more worried about the 20 MPH average because most trannys get warmer at such low speeds. My experience, rather than spend a lot of money on upgrades; pull it at night when it's cooler and see what happens. If you have problem adding additional transmission cooler is not that expensive. I also run Amsoil ATF but that doesn't make it run cooler, it just lets the ATF get hotter than standard ATF before it chemically breaks down. Sort of an insurance policy. The plastic parts and seals in your transmission still melt at same temp no matter what ATF you use.
There is one major difference between your 2004 model and mine, you have a much better transmission cooling sytem for steep grades. If I understand it correctly the 2004 DOES NOT use engine coolant as a primary transmission temp cooler. The 2001 does, so when pulling steep grades if the engine coolant begins to get hot so does the transmission fluid, the tiny transmission trim cooler in front of the radiator is way to small to cope with hot radiator fluid on the 2001 model.
On mine what I've noticed is my transmission temps will get to 160 degrees (in pan) when it's about 75 degrees ambient and I'm pulling moderately hard(the Eisenhower is much worse than moderate!). For every 10 degree rise in ambient above 75 degrees I get a 10 degree rise in transmission temp. So at 100 degrees outside I expect to get about 185 degrees transmission temp if pulling; and that's exactly what I get. In other words at 75 degrees ambient the maximum cooling I'm getting results in 160 degrees transmission temp. Any rise in ambient after that results in same rise in transmission temp. Also I pull in lockup at all times, even at 60 MPH or in 2nd at 20 MPH because that's how my ATS Co-pilot is set up and this makes for cooler transmission temps.