In riding cross country in the summer of 2008, I was faced with this situation. I decided to take a more direct route from Natchez, MS to Deridder, LA to make the connection from the Great Rivers South to the Southern Tier, instead of proceeding south to St. Francisville. "Cutting the corner" in this way saved 135 miles!
I found this route safe, with reasonable traffic and, with the exception of about 3 miles south of Leesville on US 171 (which may since have been repaved), well-paved.
1) Cross the bridge from Natchez to Vidalia on the eastbound span. I was told that despite it being against traffic, it has a substantially wider shoulder, so it is the safer side. I was fine on it.
2) Take US 84 West to just past Archie into SR 28 West into Alexandria
3) Ride 50 miles more on SR 28 West into Leesburg. Be careful to have enough water and food in this stretch - once you get west of Alexandria, there is almost nothing until Leesville, which is where you pick up US 171 South for 21 miles into Deridder. This will intersect US 190 West on the Southern Tier.