Using Car Speaker As Music Player in iPhone
If your stereo does not register that it supports the A2DP profile, then it likely will also not handle A2DP communication. It is not as simple as finding an app that will "fix the problem", because the problem is likely that your Stereo does not support audio playback. The level of difference between A2DP for audio playback and HSP for maintaining calls is enormous.

Perhaps you may be able to talk to the dealer and see if there is a firmware update for the stereo itself, something they can do to enable this feature. But otherwise, no App can solve it alone.