Have a look and see if you can get similar pricing on QR 964 (DOH-DPS) to GA 7036 (DPS-LBJ).
It's a smaller airport, easier transit and you have many more options to LBJ from DPS (normally a later GA flight as well - GA 484 - as well as a few other options including 2 x Lion Air flights) - whereas CGK-LBJ is 1 flight a day only.
Also, if you were stranded, I know where i'd rather be!