An Idea I had 'back in the day' was to use a hand free kit used normally for cheap mobiles. I never went any further with this idea than a few diagrams and such. Howver my plan was to 'hold' the screen using slim line magents from any hardware store and plaec over the top of the magnet a thin peice of metal and use this as a conductive surface for the connections. So in short youd place the screen onto the 'holder' and the magnets would hold it and create the connections for the plug, I dropped the Idea cause I frowned on the idea of having a live 12v plate in the car, if you follow.
Anyway Ive seen crazier things work from even stupider ideas.