What about a LAN connection? I believe that there is a CAT 5 cable behind the touchscreen. I'm not sure if that gets you anywhere.
Another thought that crossed my mind was setting up a wifi network (with no internet connection, of course) for your car and phone. I assume the app and/or car needs to communicate with Tesla servers. However, if they communicate directly with each other then you may have an option there.
I love the idea of using that Napier SUV tent. Not only for the climate control and the extra sleeping/storage space - but that you could leave your luggage in the car while still accessing from inside the tent, and can just close the hatch and drive the car away for day excursions with your valuables all secured.
I just bought the orange Sam's Club version of it, which is slighly larger (10 x 10), and has a rain fly that zips to completely cover the three sides not connected to the vehicle (some of the negative reviews on the regular green one is that water drips from the smaller rain fly onto the tent itself and leaks in through the seams). The side of the fly for the main tent door also has a large extension whose door can further be used as an awning with two vertical poles.
I set it up in the backyard over the weekend to try it and waterproofed all the seams for good measure. I didn't hook it up to the car, but in the photo the side that connects to the car is facing away from the camera....
Don't forget the hot dog method. Tie a string to the rear view mirror with a hot dog dangling on the end at screen height. Then fold a 3x5 card in half to make a 'V' and tape it to the middle of the string, with the two middle vents pointing at it. As the air blows, it will push the hot dog away from the screen, only to swing back and "press" the screen. Since it's capacitative, it could be a hot dog or your finger, the screen doesn't know. It happens frequently so the touchscreen never has a chance to hit it's 20min cutoff.