If I did it, you can too with your rig, assuming a decent set up, ie, good brake controller, properly adjusted brakes, etc.
I towed our trailer 34' and 7700 lbs with my 300hp F-150 at my GCWR of 15,300 lbs. I was not the first up the hills. I sometimes had to run the dog pee out of it in 2nd to maintain ground speed of 45-50 mph. And, to be sure, I had to use my brakes judiciously. But, it was fine. No white knuckles, no near misses. Don't come down a hill in a taller gear than you went up is a good barometer. When using brakes, get on them early before momentum starts sucking at you. Apply short, firm pedal pulses for a few seconds then back off and do it again. Do not ride them long-term or they'll fade. You should be fine with your rig, even with the altitude derating.
We navigated Big Horn Pass, Wolf Creek Pass, and plenty of other un-named but challenging roadways, all without incident.
Also, Good Sam, who I had a membership with at the time, had a routing service where the steep mountain grades were labeled for your consideration when chosen as a part of your route. It's pretty difficult to completely avoid all the steeper routes, even around PA. Western Rt 30 anyone?