Hey! Did you ever get this to work?
From my understanding, I think you may be going about this wrong.
This "device" I am building then should show up on the iPhone > Settings App > Bluetooth > Other Devices. I should able to connect to the device, and have it get media information from the iPhone and be able to control it
Your Arduino will not (well, should not) display on this list as it is acting as a BLE Client that is looking for your phone acting as the BLE Server.
I believe BLE Scanner is showing your Arduino as having the Apple Service because it is under the impression it is an iOS device emitting the AMS service, which is not what you are after.