I'm right next door to you in Mississippi. I can't specifically speak to those plants, but I'll tell you what I do.
I use 6 mil UV plastic
and it lasts a few years (four-year warranty) as long as you put felt tape between the plastic and anything it touches -- like the PVC frame. I fashioned a tunnel greenhouse similar to the one shown here
. I have two black trashcans inside filled with water that absorb warmth during the day and then release that warmth at night. It usually doesn't get down to freezing temps here, so the passive heating is usually enough. On the rare occasion the temps do actually get down to freezing, I have a small heater -- so maybe a handful of nights over the course of the winter I need the extra heat.