Or just install an in-car computer. They can work off DC voltage (rather than wasteful DC->AC->DC conversion, can start after the car's started (rather than when the ignition goes on), can shut down gracefully when the car's turned off, can have a touchscreen, etc etc.

Then you can do exactly what you want :)

Yeah, but where would I put one so that I could conveniently operate it in non-hectic driving conditions and it wouldn't get in the way of any of the controls or the front-seat passenger? The only place I can think of to put it is ... the car stereo slot.

Try the space in the passenger footwell above and behind the plastic trim but below the glove box. There's usually a surprising amount of space there.

Then you could install a fold-away 7" touchscreen into the space where the stereo currently lives...