iPhone 5C and Nissan Sentra iPod cable

I have a 2011 Nissan Sentra which came with an iPod connector cable, allowing me to charge my old iPhone 4S while also playing my music through the stero (with ability to use steering wheel controls to shuffle through songs):

I recently upgrded to an iPhone 5C, which of course is not compatible with the cable. So, I bought a Lightning to 30-pin adapter and connected it to the cable. When I connect my iPhone 5C to the adapter, it charges the phone, but does not play the music through the stereo/the car doesn't recognize it as a music device.

This is definitely classified as a first world problem, but I was so used to plugging in my phone and controling my music on the steering wheel - it was great! Now, I have to use an auxilary cable and control the music manually. I don't feel safe looking down at my phone every few minutes to change the song. And it doesn't display the song/artist on the radio this way either.

If anyone has any solutions, I would be VERY grateful! Calling Nissan has led me nowhere - they don't have an updated cable, nor does any retailer. Wish it was a simple USB cable! Many thanks for your help.