You have a good handle on it- there are really no restrictions on car carry. You actually do not need a license to conceal inside your vehicle; you can basically do whatever you want, in the vehicle. Once you leave the vehicle, you are good to conceal with your AZ license.
You MAY keep your other guns loaded, with one on the chamber if you want- hand and long guns. No restrictions on that.
The basic principle is called extended domain- your vehicle is considered an extension of your home. You can do whatever you want as far as carrying and concealing and general storage and handling in your home, so those same things can be done in the vehicle.
The only odd thing I would mention, just in case- and which does not apply while in the vehicle- is that you can only conceal one gun on your person while out and about in public.
Enjoy your stay here.