Im in houston, and i feel your pain, i am very hot natured, i barely wear jackets in the winter and always have it so cold in the house.
this year even though it looks tacky i put foil on my windows , all of the windows that cant be seen from the street, i swear its lowered my bill and keeps the house 5 degrees cooler.
i would reccomend a 2nd opinion on the ac unit, it could be something simple (i recently had a frayed wire that was not allowing the thermostat to control the temp), you never know.
Be sure to not try to keep your temp control too low during the hours of 5-7, 75 degrees is about what you want to put it at for texas. I have two families i am close to that own their own s/c businesses and they have recently informed me that anything cooler than 20 degrees than the outside weather is not a stable temperature to maintain. It will overwork your ac unit.
Make sure all your windows and doors are sealed.I have read, yet not tried this attic cover/cozy thing that is supposed to prevent cold air from seeping into the attic.
hope this helps.