is a high volume & not cycling attractive road. We met a cyclist from Johnson City on BRAT. See if Johnson City has a club (I think so) & hook up with the Knoxville club. We can get you to Crossville.
http://www.granfondocycles.com/club/cycling_club_leisure.html Is probably a good source for LD routing info per the Randonnuering riders there. They have a cue sheets for Mid-TN to Chattanooga on "safe country backroads" at the bottom of the page.