For the small mileage difference go south to I-40, take I-840 over to I-24 down and down to Chattanooga. I-75 north to exit 20 and US-74 up to Cherokee. Most of US-74 is four lane, the 2 sections that are not are the Ocoee and Nantahala gorges. This route keep you out of Nashville, Knoxville & Pigeon Forge, Gatlinburg. IMHO US-441 thru the park is a better choice than US-129 around the south edge.
Towed our 35’ 5’th wheel up US-74 from Chattanooga several times with a 05 3500 Chevy without issue.