I have been traveling west from Tallahassee since 1973. Your route sounds good to me. Last year we left on May 1 and traveled west on I-10 (& I-12 to avoid New Orleans)to Lafayette, LA. where we took I-49 to Shreveport. Then North on US 11 to village of Ida where we took US 59 to Queen City TX. We went through Texarkana on US 59/71 and intersected with I-40 at Ft. Smith/Van Buren. We went on to New Mexico before turning north (we were going to Alaska), but I have used your route and it is fine.
We usually come back east on either I-70 or I-80, then to Kansas City, St. Louis, Nashville, Chattanooga, but we return to North Carolina not to Florida. Sounds like a wonderful trip. Enjoy! lizzie