I Pulled a TT with a huge SUV 4 years ago thru the mtns...bad news...white knuckle experience all the way. Up may be slow, but not an issue as you chug along...coming DOWN with 18 wheelers pushing your butt and blasting your left side, no exhaust brake, not so much fun.
Had enough fun. Bought a 2500 turbo diesel. No issues anymore. Skin looks a lot better. Wife and I actually "talk" as we traverse the hills.
Just remember, hills out west are a heck of a lot different than NC. You likely will be fine if you just stay within your trucks abilities. We are retired and wanted to have the set up to travel any reasonable roads in the US of A and possibly Canada. AIN'T doin Alaska. Not going there in any RV. Nope. Flying in, renting a car and drive into the pot holes of the world. Hotels can sometimes be very relaxing
Be safe, have fun.