Here is the results of my sleepless night…
I will leave Tucumcari for Amarillo (117 miles) and rent the car in the middle of the day.
I will then drive to Corsicana (435 miles) and back to Wichita Falls (220 miles).
I will sleep in the hotel room that I rented via Travelocity and drive the remaining 4 hours to Amarillo tomorrow morning, return the car at noon and only be charged for one day.