L-L-C, I only get up to the Knoxville Area once or twice a year, usually to hunt Big So. Fork, so I'm not a real expert on E.TN shooting opportunities. However, check the events board on this forum and there's a monthly flintlock shoot in Winfield TN (up near Oneida or Sunbright). Blanket shoot, pre-1840 dress required.
French Broad LR over in Marshall NC ought to be within 100 miles of Knoxville. They host a 3 day W. Carolina Offhand Championship July 10-12, if you like paper punching. In Oct they will put on a 3 day primitive 'vous with woodswalk, seneca run, etc. And, I'm pretty sure they have monthly matches as well. (I saw your other post that said you're in Del Rio - that puts you 30 or 40 miles of the French Broad club. If interested, I'll email you the club's POC's email address.)
For a longer drive, Davy Crockett Longhunters in Lawrenceburg TN has a 3 day April 'vous, and a 3 day Crockett Days 'vous in early August. Good people, traders row, and good times in general, although since it's held in a State Park, the flatlanders can come and go at all hours.
There's probably other opportunities, but I'm down here in Panhandle FL, and those are all that I'm aware of. SCL