I know you don't want something sitting out, but wouldn't you need some way to control the bluetooth receiver for pairing or re-pairing? I know everyone here always tells me that bluetooth never fails to make a connection, but that simply hasn't been my experience. Fortunately my car has bluetooth built in, so if it doesn't connect when it turns on, I can go into the menu and tell it to try again.

When I was trying to use my phone for both audio and phone, I used this device (with a cable, not the FM tuner), but that's far messier than you want.