Chattanooga is about 200 miles from Joe Wheeler. Joe Wheeler is Mile No 277 I think.
With shorter daylight, it could take 3 - 4 days. Summer time is 2 long days total.
Goose Pond Marina is a great 1/2 way point. Two short days would put you on top of a dam, I dont remember which one though but there are 2 possible places on your right to anchor out. or you could try to make it a long day to Goose Pond.
Then from there, to Wheeler can be broken into 2 days with Ditto Landing in between or just another really long day.
It all depends on your speed and how comfy you are in the dark with radar.
I dont have radar, so I need to be more careful in my planning.
Hope this helps.