I had a similar problem. It was the underlying cause of what I reported earlier.

The real reason is that my car is a bit slow at switching to sound input from Bluetooth. Merely being paired is not enough, there must be an actual sound stream coming from the paired device, only then will my car's stereo offer me the option to switch to it. So I have to start playing some music on the phone, switch the car's input to it, stop the music, start WhoGo... not ideal but it works.

Another option is to unpair but unfortunately it does not always work, voice is still muted. As if the phone thought it was still paired and tried to stream the voice through Bluetooth. I have not quite figured out what the pattern is. Closing and restarting WhoGo does not always help either. I will try your re-routing workaround the next time.