I'm sure you know the roads across northern Arkansas better than I do, but it looks like you could pick up I-155 near Haiti, MO and go over to Dyersburg, TN (that part I am familiar with, as we follow that route into Kentucky). US 412 will take you down to I-40 at Jackson, TN. I-40 will take you all the way to Knoxville, TN (through Nashville). Actually you can stay on I-40 all the way to Kodak, TN which is just north of Sevierville.
We always enjoy eating at the Apple Barn in Seveirville. There a couple of very good campgrounds in Seveirville.
This is just one route possibility.