I am not an iPhone person, so I will approach this from a theoretical position. I faced the same challenge on my Android devices. It is very frustrating, so I know what you are going through. My solution was to load a 3rd party app that sort of sits between the device operating system and the uconnect radio. So when I press "play" on the radio, the app on the phone pops up and askes me which app on the phone it should route to the Bluetooth. It took some trial and error, but it works well enough to solve the problem. Perhaps there is a similar apple app?
For comparison, here is the app I use in the android world: https://play.google.com/store/apps/d...ni.android.mbr