There really isn't a nice way to get to Townsend which is one of the reasons it stays a nice quiet spot.
I don't think the traffic on 66 is bad enough to justify going all the way around through Knoxville. 321 cuts off 66 before you get to the really bad section where traffic is the worse.
Two alternatives is to take exit 432A to catch 411, catch 66 south for about 4.7 mile than 321 over to Townsend. Avoids 8.6 miles of 66.
second choice which is the way I go with my TC because I don't mind slow drives and the scenery is pretty is to catch 321 at exit 440 to Gatlinburg, catch 441 to the left and fight the dozen blocks of traffic in town. Once out of town, take the right at Sugarloaf Visitor Center over to Townsend (I usually go to Cades Cove). Doable in a trailer if you don't mind county type road that curves around a lot as it follows the river (as said earlier, I usually do it in a truck camper but wouldn't hesitate pulling a trailer though a lot would recommend against it)