I'm poking around maps.live.com looking for alternative routes between Tupelo and Huntsville. The fast way is to take 78 to Hamilton, 43 to Russellville, 24 to Decatur, and I-565 to Huntsville..........................

route 3 and 7 are not paved. lots of loose gravel. great for a dual sport.

I would personally avoid them on a road bike. I am not sure about Thompson Creek, but if it goes anywhere near the Sipsey Wilderness it is gravel. If it goes through at all.
There are not a lot of East West road through the Bankhead. The only one that come to mind is 60. I been down part of it in a car. I remember thinking it would be a nice ride on a bike although I reccolect the pavement was a bit rough.
You could run the Natchez all the way to Alabama. and then take CR 21, then up 247 to CR 49 to Russelville. then pick up the Wilderness Parkway. One thing you should know is the absolute fastest way from Tubelo to Huntsville it to take the Trace to Hwy 72. But I am sure you know 72 sucks.
But you want to make halfway decent time.???? how about this. in Hamilton, take 278 East to Addison (the fast part)
In Addision starts the fun part. Pick up Hwy 41 North in Addison.
41 to CR 1101. Turn right at the church. Doesnt look very good at first but this is a great road. Stay on it until it ends at Old Hwy 31 (CR 1223)
Turn left on 1223. Stay on this all the way to Hwy 55. It crosses 31 and changes names but stay on it.
Turn right on 55 to the town of Eva. Turn left at the light onto hwy 73.
Go down the hill past Brewer High school. Though the light in Florette all the way to Hwy 36.
Turn right on 36. Stay on 36 until it ends at 231. Turn left into Huntsville.
Have a good time
Yankee Dog