DavidF, I added AC to my '57 this past summer. We live in AZ, so I had some of the same concerns that you have living in TX. I tried to get mine bulletproof at 115 degrees. A few things that I learned in the process...
I was stubborn and tried to keep the generator in spite of all the advice on this website not to do so. Yes, you do need an alternator. Don't even think about keeping the generator. I won't forget this as I tried to solve a dead battery issue on a searing hot August afternoon with heat in the desert at about 118. Being stubborn has a price...
I ran a three wire alternator and used the BAT terminal of the voltage regulator as a junction terminal for the voltage sensing wire of the alternator. Ran the AC off this terminal. The other terminals of the voltage regulator are empty, but this allowed me to keep the stock look of the voltage regulator on the firewall.
I used two electric condenser fans hidden behind my grill. These were wired with relays off the compressor...when the compressor kicks on, the fan relays trip and fire the fans. A local hot rod shop showed me the trick of wiring the fan relays off the compressor. The compressor is wired as normal through a switched relay.
I converted the stock 4 blade fan on my 235 to a repopped 6 blade high volume fan. These were a factory option back in the day for stop and go city driving or heavy agricultural applications. I went with a repop after reading about folks who had installed old fan blades with hidden flaws and ended up throwing a fan blade through their hoods. All OEM 6 blades that I found were...well...old...and untested under stress. So I went with a new repop.
The combination of the 6 blade fan, two electric condenser fans and alternator handled my AC and my cooling at peak times in the AZ desert. I needed the entire combination at peak.
I kept my cab stock and did not insulate it. That means the AC unit is trying to heat a hot tin can in the summer AZ heat. It takes the edge off, but it ain't exactly an igloo. Outlet air off the evaporator vents is as cold as it can be without frosting the coil, but refer to the hot tin can statement above. Keep your expectations realistic.
Please get in touch if I can be of any help.
Maybellene