yes,  i have canoed the big south fork's middle section.  this section is great for canoe-camping and  takes you from tennessee to kentucky through some gorgeous scenery in a national forest area.

if you start at leatherwood ford and go to blue heron, its about a 27 mile trip or so but you can make it a shorter trip by stopping at station camp.  if the water is running good, its a long overnight trip, but we did it as a nice 3 day/2 night trip and took our time.  its a beautiful river and part of the national wild and scenic river system, i think.  there are 2 nasty rapids on this section that are clearly marked and easy to walk around, but the rest of the section is basic river shoals and a few riffle type rapids.   i guess they are class 2 but they are not anything special.

this is a free flowing river, so if you get on it when the CFS is really moving, all of the above changes and it is likely a whole different river.  one nice thing is that it is able to be paddled at low flows, so you can still do it in the summer when most of the other rivers on the cumberland plateau are dry.  

i've never been on the lower section, but i am sure that it slows down some.  

the only real drawback to the river is that it is a long (more than an hour) shuttle from the take to the put in.  there is a good outfitter up there called sheltowee or something like that who will shuttle your car if you want.