Virtual Audio Cable for Android (not!)

I want to be able to listen to the receiver in my shack while doing other things around the flat. I wanted to do it with a Bluetooth headset paired with an Android smartphone, so I need a simple "virtual audio cable" app that pipes the audio from the physical micrphone over to the BT headset. The app could also provide additional functionality, like squelch or CAT control or even the ability to reply and transmit.

As of today I have not been able to locate a suitable Android app. I tried to build one myself using MIT's App Inventor, but their Bluetooth library supports data transfer only, not audio (August 2014).

I will have to use a stand-alone headphone+base. They cost about 10€ in Far East but they transmit in the FM broadcast band, which is not license-free in Italy and it is too crowded for any low-power signal.

Case closed.