I'm not sure if bluez currently accepts sending anything other than SBC over the a2dp link. E.g. when I was working on the DSP encoder it wasn't afair possible to even send MP3 (which some headsets can decode directly).

Things may well have changed now though, so we should probably look at the upstream Bluez project to see what's possible.

Out of interest which headphones are these? Mine only decode SBC, so not much motivation to look at anything else.