I've driven Ashville, NC I-40 many, many times over my lifetime. I driven it with 18 wheeler semi-trucks to a motorcycle. I once crossed over (from Morganton, NC to Indianapolis, IN) with a 1972 Oldsmobile towing an 18 foot U-Haul covered trailer loaded to the max and crossed over just fine. I towed with my 1500 suburban towing my 18 foot Dutchmen Sport Travel Trailer (see my profile on the right - click the link), to my now 3500 diesel pulling my 36 foot Outback.
I will say, I was able to climb that mountain at 70 mph with my motorcycle, and 95 coming down! Oh that was sweet!
My Oldsmobile limped to the top (from the Piedmont side) pulling that trailer, but made it (that was back in 1979. I towed my daughter's car with my 3500 gas duly over that same mountain when she was stationed at Charleston, SC in the Navy. (2007)
We just crossed over that same mountain twice this last December pulling our Outback.
Bottom line ... with your 1500 you can do it. But you do not want to tow in overdrive. Pull the trailer in Drive. Going up those mountains, drop down into the next gear lower and just keep moving forward. Keep the RPM's up on your truck. When you can move to a higher gear, do so. You can probably cross over about 50 mph. Don't be intimidated when everything on the road is passing you. Some spots on that section of road have truck lanes (far left prohibited from trucks). Where those appear, move right. You'll be fine.
If your truck does not have a "tow haul" mode, coming down hill, use a lower gear and let the engine do the braking for you so you won't burn out your breaks. Break only enough to slow down, then down-shift into a lower gear to maintain a SAFE down-hill ride.
You'll have no problems, just use your head and don't let other traffic on the road intimidate you.
(I absolutely LOVE that stretch of road from Knoxville, TN to Morganton, NC. Especially the Ashville area.
Do you know that Ashville, NC is Billy Graham's home? He has a home on one of those mountains.