Buick LaCrosse 2014. Buick-Intellilink-Bluetooth issues

Hi,
I paired my current iPhone 5S about 16 months ago, this was my first Bluetooth device, while other devices have been paired previously by the first owner (dealership).

I enjoy streaming internet radio stations (e.g. Radio Tunes – app-/ platform, usually provides a very powerful Internet stream) from that iPhone “into” my Buick Intellilink! There were problems from the beginning, even thought I live in a large city, have LTE and a high Signal strength.

Here is what happens: Sometimes my iPhone 5s books in immediately, before I have pressed the vehicle`s start button, however sometimes I have to manually connect through the “device Management” – menu on the touch Screen to hook up Intellilink with my 5s.
Now, once this is accomplished, sometimes my Internet Radio Station (eg. smooth jaz 24/7) can be heard loud and clear, but frequently, it goes away and then comes back even though the mobile Signal strength is still strong and LTE is still available and no “buffering” is going on (latter does happen in fringe Areas and then the stream breaks off).
Occasionnally, I do stop and restart the iphone from scratch and eventually, i can readio -stream then, but not always!

Bottomline is, for no obvious reasons, the iphone is Bluetooth connected, but the internet Radio Streaming will not work, although you see the stream is available as seen on the iPhone -Display. If you turn off the car and thus disconnect the Bluetooth Connection and Buick Intellilink, you can hear the Internet station fine through the phone`s Speakers.

What is the Problem here? Anybody with similar issues?
Any help or idea to resolve the issue is appreciatied!

Best ,
Klaus

PS: Apple car Play was introduced for the Lacrosse for the 2016 model year, mine is a 2014.
Can Car Play be installed (uploaded) for my 2014 Radio/nav unit or will the whole unit to be Exchange for a 2016 unit with the front touch Screen. Latter Option probably is very expensive, but would replacing the 2014 unit for a fully