A few weeks ago I learned that you clean the headband contacts. Mine were dirty but not corroded like in the video here. Given that I now get full stereo with a wired connection, the headband is probably not the issue. 
Discussion
The bluetooth component can be replaced, though it's fairly expensive and tedious (three different screw types, because Apple...). And I don't know for sure that's the broken part, what caused it to break and if the root cause will just keep killing off components.