I've (re-)imported the changes made to Pulseaudio in Ubuntu 16.04. This primarily improves the experience of using Bluetooth headsets with the phone. However, there's a report of regression due to these changes before. I've fixed that one specific regression, but I'm not sure if there's any other regression due to these changes.
Please only test this change on a device running the latest images from the
devel channel, and test responsibly! In other words, try it on a spare device or when you know you'll be near a computer you can use for reflashing. 
To test, please follow the instruction:
- Mount a tmpfs so apt can breathe:
sudo mount -t tmpfs tmpfs /var/cache/apt/archives
- Install the repository:
sudo ubports-qa install xenial_-_pulseaudio-updates-to-0ubuntu3.10
- Reboot your phone.
See if there's any regression in both built-in speaker, wired headset and Bluetooth headset. If possible, use a Bluetooth headset that can be in both music mode (hi-fidelity audio) and call mode (low-latency 2-way audio).
You may want to also follow this test plan from Canonical if you want to be extra sure there's no regression: https://wiki.ubuntu.com/Process/Merges/TestPlan/pulseaudio
Note for OnePlus One users: It's been reported that Bluetooth on OnePlus One is unstable in general. Thus, you may want to skip testing Bluetooth on this particular device.
Known issue: The issue that the playing streams won't switch to the headset after a re-connect is known, and will be fixed after this .
 This specific instruction courtesy of Dalton Durst.