Towing mountain grades
I had a 2013 2500HD with the 6.0 liter with the dual fuel CNG option. It pulled my Montana HC 325Rl ( about 8900# dry) just fine( not using CNG to tow). I live here in Utah and can't drive anywhere north, south, east, or west without pulling a steep grade at some point. Did it with that Montana with no problems. I didn't have the 4:10's so you'll pull the grades just fine going up. If your trailer brakes are adequate and adjusted, I never had a problem going down either. Tow/Haul mode with the grade braking is definitely helpful. I went to a 1-ton Duramax in 2016 when we switched to a bigger 5er. The recommendation to have fresh fluids and synthetic is a good one. I'd do the trans, xfer case, front/rear diff's as well. If you have time, take scenic byway 12 from Torrey down through the Grand Staircase. Highway 191 from I-70 down through Arches, Canyonlands, to Mexican Hat has great scenery. It's really crowded here anymore in the summer so be patient in the Nat Parks. Enjoy the trip.