oops - rereading your OP - one option to would be to take the MRT north to Vicksburg (you'll have to catch a ride across the river though unless you cross in October on the day of the Bricks and Spokes ride) then head west on US 80 - low traffic due to being parallel to I-20. you could also stay on the west side of the river from Vidalia/Natchez and take some local roads from there north along the river to Monroe or head northwest towards Shreveport.
mike