Keeping ease of customer installation in mind, the better product would be one where the customer simply unplugs the FDP-Link III + power cable from the screen, plugs it into the new PCB, and the new PCB will have its own identical FDP-Link III + power cable that plugs into the screen's original port. The new PCB would have its own FDP-Link III serializer + deserializer and have a default mode of pass through. There would be custom modes where the pixel data going to the screen is overridden with android auto / carplay / custom input data. These modes would likely be toggled using a button, and the last-used mode saved so that the unit starts off exactly how you left it.
All of that is much easier said than done. Next step is to find out if any FDP-Link III breakout boards already exist. The perfect existing product would be one that breaks out video data, and touch input data from the FDP-Link III connection.