If you really wanted to get creative and had some programming knowledge, you could create a serial interface, with a small touchscreen monitor, to make selections and to actually see what songs are available, basically taking the place of the old lcd panel and keypad and working as a 'modern' wallbox.
Using the amp may not be ideal, when you want to connect the system to the line-in on your car stereo system, but you should be able to tap into a line output on the amp and then just not connect speakers to the amp.
A 400 watt power inverter should supply the power it needed.
I used to have a '75 olds delta 88 royale convertible, spent probably two years restoring. Grinding, sanding, bondo, fiberglass, priming, new white top installed, and then off to paint: viper red, with silver metallic. When it was restored, it looked like this one:
I've got an itching to get another car and start working on it, but there's no way I can afford it right now with all of the other projects going on. Maybe in a couple years.