I've done the Beech Gap to Tellico River section dozens of times in the last 15 years and all of them as backpacking trips. In fact, you could probably do this section in one day if desired---but what's the fun in that?
** Beech Gap to North River road crossing. Leaves the Cherohala Scarway and climbs up on 5 or 6 switchbacks to the top of what I call Festus Knob (and used to call this knob John's Knob but I was wrong). Descends to NR road crossing.
** Up to the Rock Quarry and steeply down to Mud Gap.
** 1.5 mile climb with 500 foot gain to Whiggs Meadow. Go to the top of the bald and further down to the northwest and you'll see a Pond---a decent swimhole in the summer. There's also a spring water source up above the Pond if you know where to look.
** Go into the woods on the south side of the Whigg and look for a memorial cross with pictures.
** Leave the Whigg on the BMT and pull the 3,000 foot loss in 7 milles to Tellico River. You're done. There are two very nice and secret campsites on this section paralleling Sycamore Creek.
Here are my Keyworded pics of your route, starting at Beech Gap---
https://tipiwalter.smugmug.com/keyword/beech%20gap/
This next set shows the Rock Quarry south of Beech Gap---
https://tipiwalter.smugmug.com/keyword/rock%20quarry/
And then comes Whiggs Meadow itself---
https://tipiwalter.smugmug.com/keyword/whiggs%20meadow/
And then the Sycamore Creek drop off the Whigg to Tellico River---
https://tipiwalter.smugmug.com/keywo...amore%20creek/
And then around Tellico River by the Fish Hatchery---
https://tipiwalter.smugmug.com/keyword/fish%20hatchery/
SIDE NOTES
** Once atop the Whigg if you leave the Whigg on the BMT and go about a quarter mile north there's a faint side trail on the right to the top of Haw Mt (and a back way to get into the Snowbird wilderness) which is at 5,500 feet and the highest mountain in Monroe Cty, TN. In the winter you get a good view off the Haw down to the Whigg.
Here's a view of the mighty Haw Mt as seen from the top of Whiggs meadow. To the left of the Haw is the BMT and the sidetrail to the top of Haw climbs that gradual ridge to the right.
Here's a view of Whiggs Meadow as seen from the Haw.