keep in mind the following: in TX it is legal to have a gun in your vehicle if you have a license or not. It must be concealed, but you can have it anywhere, even on your person as long as you're in your vehicle. Because of this law, many LEOs will ask "do you have any weapons in your vehicle"?
It does not have to be unloaded, the magazine can be full, and in the pistol, and one can be chambered.
Aside from that, you're doing right by checking all the rules that you may be faced with prior to traveling. So far everything I've read in this thread re: TX is correct, just thought I'd throw the extra info in.
PPQ M2, G-19, PT-140 Pro, PT-111 Pro, Core-15