I used to drive semi trucks in the 90's: 200HP truck with 20+ tons of cargo, so about 30-32T of total weight. You couldn't see the hill yet, but the truck needed downshifting. Boy, do I miss the double-clutching...
There is something to be said about liability when driving with extra weight: leave yourself some space.
There is something to be said about wearing out the transmission and axles when driving with extra load for extended periods of time. It does put extra stress on the engine if you floor it for hours on end to keep up with the traffic. Will one trip trash your truck? no! would I drive it somewhat overweight myself? I sure would. However, if this was my regular gig (e.g. doing this monthly, on a similarly long distance) I would upgrade to something bigger. I tow an RV trailer (~4000lb) a few times a year and I'm glad I got the 2500 with a V10. Hardly ever do I need to floor it on up-hills. Would I still tow it if I had a smaller truck? you bet. I would just take it easier.
If you have the option to do it: try driving at night as much as you can. The air is cooler and that helps to keep everything cool (engine, transmission, axles), it does help with engine power, especially at high elevation, as well as the gas economy. You're unlikely to run AC at night, too. And you'll have less traffic to worry about. At night it's mostly truckers on the road (I wonder why???).