Here are a few Gravel roads I would not recommend except on an enduro type bike.
Joe Brown Highway. AKA Unicoi Turnpike from Coker Creek off TN 68 to the Hiwassee Dam Turn Cutoff. Attempted on motorcycle a few times and turned around both times. Did it in the car and found I was glad I didn't get too far on the bike.
Witt Road. A gravel road that runs from TN 68 near Tellico Plains. it runs a close parallel to TN 68 but it is rough, seep, and you have to forge 6 streams: have done on car a few times. It is 8 miles through the Cherokee Forest wilderness. You can see bikes trying this road on You Tube.
Tn 32 from the US 321 cutoff in Cosby is a very twisty road: I think better than the Dragon, but with a twist. One you have to watch for lots of road debris from trees, rock, etc. It is paved all the way to the NC State Line and the Appalachian Trail. Here it becomes Mount Sterling Road and for 1.2 miles it is gravel. Light mostly. I have done it on motorcycle many times. Waterville Road will take you back to I-40 to exit 451.
If you are brave, you can continue on Mount Sterling road: which roughly parallels I-40, and it will drop you into. Cataloochee. It is about 14 miles, but takes over an hour on a motorcycle. Once in Cataloochee, you find paved roads. Eventually the paved road ends and you have to take the Old Cataloochee Turnpike/Cove Creek Road back 3 miles on a gravel road until you reach pavement again. Then it is another 7.5 miles back to US276/Jonathan Creek Rd near I-40 exit 20 in NC.
The Cataloochee trip, IMHO, is the best as road within the park is in pretty good shape and gravel is not thick at all. One thing though. Seasonal closing of the road is common in winter. but if it is open, you get to see large herds of Elk within Cataloochee as well as well preserved homes and farm building from when this was a farming community.
Here is another. NC State Highway 197. Although it is paved on both ends, from Exit 15 on I-24/US19 to Burnsville at US 19E, In the middle through the mountains it is the only NC State highway that is still gravel within the Pisgah National Forest in Buncombe County, NC. It is a 4.5 mile stretch. I have done this on motorcycle several times. It was not thick gravel.
Hope this helps some. Oh. No not tried these on the new spyder, not until I get the missing belt guard anyway