You honestly won't have a problem!
In December, my husband and I relocated from Jacksonville, NC to St. Louis (so we took literally the same route as you're taking- just a little further for us) with a 26ft Penske Truck with Car Carrier (with my husband's Camaro on it)!
I drove my car and my husband drove the truck. Honestly, going
up through the mountains around Asheville was the difficult part for DH- he could only get up to about 25-30mph! Going down mountains though was never a problem, and he never felt unsafe- he actually appreciated the fact that gravity sped him up 'down' the mountains as it helped him get 'up' the next mountain with less difficulty! He also said that he far preferred the Penske truck to U-Hauls he's driven in the past- it seemed a lot better maintained to him.
The biggest obstacle of the entire trip we actually encountered was probably navigating into our street, and then the Penske truck into the driveway. You'll be absolutely FINE!
P.S. You'll have zero problems around Paducah, it's a complete non-event!