The distances involved in the original route are long compared to European or densely settled eastern/northeastern US notions, but are pretty much just a trip down to the grocery store for many in Texas.

The eastern part of the trip may not allow quite the long-legged jumps, although the last time I was through that part of the country it looked pretty much the same to me. (My last trip was some years ago, from Philadelphia to Dallas and on to Wichita KS, which I did in one day. - - But it was about a 39 hour day as I recall, in a VW beetle that couldn't quite hit all the legal speed limits.)

Distances are long enough that each jump from town to town, with loading up, unloading, settling in and unwinding from the drive will be about a day. You might, if your endurance is really good, work in a light entertainment the evening of arrival in a new town at some of the stops; but I'd say the emphasis would be on "light."

Travel will take most of 8 of your 15 days, leaving 7 days for visiting at the stops.

Nashville is probably the stop to drop out if it really is necessary to cut the distance/time (if driving time is the only consideration), since it's at the "far end" from the starting/ending point and the only convenient route requires retracing the Memphis - Nashville - back thru Memphis to get to the road to Jackson Mississippi. The Nashville to Jackson also looks like about the longest single-jump drive, but I didn't print out the whole trip ticket. Memphis to Nashville is 212 miles, about 3:45 driving time, which you would retrace back to Memphis on the way down to Jackson. The drive for that day - Nashville TN to Jackson MS - would be about 420 miles, and close to 8 hours total driving time.

If you went only from Houston to Nashville and back to Houston, by almost any reasonable route your driving distance/time would be about the same as for the original plan if you allow for rest and potty stops at places where you'll find good stopover facilities. Dropping any of the other stops wouldn't save much in driving time, since the rest are pretty much on the routes you'd take anyway, between Houston and Nashville and back to Houston.

Houston to Nashville via Dallas isn't much different in distance than Nashville to Houston via New Orleans, and the roads should be pretty much comparable as to speed and comfort on either route. Memphis to Nashville and back through Memphis is the only "retraced" part of the original route.

John