Modifying an old phone to draw less power?
You'll need the phone transmitter to be constantly on and that's what draws the main share of power. You still can remove stuff like LEDs and backlight to save a bit. 

Regarding not killing your battery - you have to choose the charger to be power efficient. Those can vary in terms of quality and efficiency quite broadly. Then you have to measure the amount of current the setup draws and depending on how frequently you drive your car it might be no problem after all. Typical car battery capacity is around 100 amp-hours, if your setup draws, say 100mA @ 12V and you drive every day, you should be ok.