I40 west to 840, in Tn. Take 840 west avoiding Nashville. Take exit that says Natchez Trace or hit I40 again and then hit the Trace. First exit takes you a bit on local roads.
Speed limit is low but you get there faster. Get on I20 near Jackson Miss.
I understand ,one, of the National Park camp grounds, on the Trace, will now handle big rigs. Make by there before you want, to stop, go to Poverty Point ten miles off I20 in La. Great Place to stay before you hit Texas about 4-5 hours later maybe. May not be the fastest but I haven't timed it.