271 thru Paris and Tyler. Then south on 69 out of Tyler down to 79 over to Cameron and Hwy 77. South out of Cameron on Hwy 77 into Harlingen, then west on 83.
I think this would be an excellent choice. I live in East Texas and am familiar with every mile of the route above. It not only avoids Dallas/Fort Worth, but also Austin and San Antonio. I have found Austin to be the city I most want to avoid traveling through.
I will mention one other possibility because that is the route we would take through Oklahoma. Stay on down to Fayetteville and Fort Smith then pick up US 259 all the way to Henderson, Texas then join US 79 as above.
A variation on the US 259 route would be to take TX 155 near Ore City (where we live) and go through Gilmer to Tyler and on to Palestine, Texas where you would pick up US 79.