Playing music over Bluetooth in Android car unit that only accepts Bluetooth phone call
Really, the best method is to just get a Bluetooth adapter from Amazon or something. 

More apps can be integrated with regular Bluetooth and you will still be able to use the Bluetooth thing built into the car for calls. On Android, there is an option to choose what a certain bluetooth device is used for.

This would also be better than any hack or workaround because it will always be in a 'call' and will probably drain more battery. Also, an app cannot intercept all audio (which would be needed to send everything to the speakers) unless your phone is rooted.