This is one of those "You can't get there from here" situations. edm3rd's suggestion of U.S. 65 is a good one. U.S. 65 to Tallulah, across the Mississippi at Vicksburg on I-20; east to Jackson and south on I-55 to The Big Easy.
Of course, a much more scenic and historic route would be to stay on U.S. 65 to Ferriday, LA, cross the river at Natchez and you have a choice to go directly east to I-55 via U.S. 84 & U.S. 98 OR take U.S. 61, a.k.a. "The Great River Road" & "The Blues Highway" all the way into N'Awlinz... or you can bail at I-10 in Baton Rouge. WHO Dat?!
Full Disclosure: This is the perspective of someone who is retired, doesn't punch a timeclock, who travels *with* the dogs & cat (no boarding) and can "plan" to leave the house for a week but can extend it to two weeks -- or THREE! -- without breaking a sweat. Your mileage may vary. ;)