Last summer I visited a friend who lives about an hour south of San Antonio. His house was just awful. Hot all day, never quite cooled down at night.
We went out and bought sheets (4' by 8') of 1" thick foil-faced polyisoocyanate insulation. R7.2 per inch.
Polyiso is far suerior to thin, flexible, bubble foils that are advertised as radiant barriers. Eventually, the foil face may get covered with dust. The dust-covered PI will still act as a radiant barrier, the dust-covered bubble foil will merely be a conductor.
We used nails with 3" metal buttons to fasten the sheets to the rafters. You only need a few nails per sheet. No need to be concerned about the sheets breaking over the rafters, either.
When you install the sheets, gap them by about 3/8ths of an inch from each other. After the entire attic, roof and gable walls, are covered, use canned foam to foam the gaps between the sheets. This will make the installation air tight.
On the day we started, it was 132 degrees in the attic. The next day, which was just as hot, the attic temp was 77 degrees.
His house already had soffit-to-ridge vents in place. We also used canned foam to seal any penetrations in the attic floor.
I live in CT and use a lot of polyiso up here as well.
For your blown in insulation, consider blown cellulose instead of blown FG.
Not sure how it's sold in Houston, but Homasote and Celotex both make PI. Marketed as TUFF-R and ULTRA-R. Call your local lumberyards and ask for "foil-faced polyisocyanate insulation". If you get silence on the other end of the phone, call Hoomasote and Celotex for distributors in your area.