Not sure if that OEM Stereo has the input for the backup cam, however I also bought a 2014 Challenger Shaker w/Manual Trans. Replaced the entire stereo with the Kenwood DNX691HD and added Datalink Mistro (OEM interface), which keeps all your OEM features like uconnect and your steering wheel buttons that control the radio can be bound to your likely i.e Siri on your phone.
Its a really great system, has Garmin GPS, and you can also add up to 2 cameras, backgrounds and more... I used this method and was able to install the back up camera and it worked with my park sense along with toggling on when shifting into reverse.
Other cool features with my replacement system is that I can watch dvd's, toggle back up camera while driving, and also brings up an OEM screen with all the computer gauges you could ask for about your car.
Cost $1,400 w/programming and installation.