I like the map; but still prefer I-40 to I-10 going to TX. I-10 is rather boring between El Paso and Midland; however, the highest speed limit you will see is between El Paso and Pecos. I think it was 85 when I was there last. It is boring though, flat and looks the same. Dodging tumble weeds may keep your interest with the winter prairie winds. At one time I had friends in Prescott, so I would drive there from LA the first day, then through Sedona, Flagstaff, ALBQ, and spend the night in Amarillo. From there I would take 287 through Wichita Falls to Decatur and cut over to Denton. I went down to Dallas from there, but for Plano I would keep going east of Denton to 289 and down it through Frisco to Plano. However, the I-10/I-20 route is an interesting experience of vast sparsely occupied space that one should experience at least once in their life.
Hot Springs is a nice stop just off I-30 on the way to Memphis. Memphis and Nashville have done well revitalizing their downtown areas; they are alive after 5 pm. The Smokies are primarily visited via Pigeon Forge (families with kids, Dollywood) and Gatlinburg (more adult, antiques) and it is slow going through them to get to the Park. There is really nothing quick about visiting the Park as you visit one site and another, it is best as a destination in itself for several days. The Biltmore in Asheville is an easily accessed destination from I-40 and I-26 goes from there toward I-81 and Bristol. If you like NASCAR, then Bristol is an attraction itself.
I-81 through VA is just plain beautiful, with sites all along the way and history galore. It runs the length of the Shenandoah valley, with the Blue Ridge Mtns on the east, Appalachians on the west. North of Roanoke the BR Pkwy runs rather close to I-81 so it is easy to drive along the Pkwy while time allows. I-64 cuts over to Charlottesville if you have time to visit Montecello. Our favorite part of the BR Pkwy is Skyline Drive (I-64 to Front Royal, and especially towards the Skyland area near Luray. If we didn't head to DC, we would go to Winchester and cut over to Harpers Ferry for some history, then up Hwy15 to Gettysburg. From there you can get back on I-81 at Harrisburg.
In general, I would tend to favor going east along the southern route and return the northern. By Jan, the south tends to get wintry weather in the form of ice; even snow will melt and form ice overnight. Whereas in the north there will likely to be (all) snow and the roads plowed routinely. The south tends to be sparse on snow plows. I-70 is beautiful in the winter and the LX handles the snow quite well. I find even the plains interesting with the hills, ranches and farms. The biggest problem I have noticed in the plains are their blizzards when roads get shut down and cars and trucks spin out of control and are strewn across the median and shoulders. Drivers in the north tend to be careful and know how to drive in the snow. People in the south may not be as careful, especially while enjoying the traction with 4wd, but not realizing that they have no advantage over others in stopping. So be careful and watch out for the other drivers.
With the LX, I have been less concerned about weather conditions because it is so capable. Thus you can pick the route that fits your schedule best and those you want to see along the way. I bought my first LC for a winter trip to Colorado and it handled all the weather conditions with ease. On my return my salesman asked me how the LC handled the trip and I told him it was uneventful - weather conditions were a non-event compared with other vehicles I had owned, because it handled all I faced with ease. It is really that good. I tend to judge how I want to deal with weather conditions by the traffic and how other vehicles will fare rather than how the LX will fare.