That is impressively convoluted. I have a feeling it ought to be possible to write a gstreamer plugin to do this, but it’s one of those minor projects that never got over the do-I-care-that-much hump.
I've got a feeling that by the time an audio stream gets to GStreamer it's not in the original format. Also you'd have to get an A2DP sink working (to make your phone think the computer is a headset / speaker)