BCM2835 has two UART interfaces available - one "stable-frequency reliable UART" and one "unstable-frequency not-so-reliable UART". Currently, ZeroPhone re-maps the "stable frequency UART" to the GSM modem, because GSM has a higher priority in the project. Bluetooth, in turn, is re-mapped to the "unstable UART" - and that's where it stops working, I didn't really look further, though here's something that looks like a solution. 

Can you help with getting Bluetooth to work in the basic configuration, as it is? Instructions:

1. Get a Pi Zero W or a Raspberry Pi 3, upload Raspbian on SD card, boot it and log in
2. Add one line in /boot/config.txt: dtoverlay=pi3-miniuart-bt
3. Reboot, check that "hcitool dev" doesn't list any Bluetooth adapters anymore
4. See how Bluetooth can be brought back to life, and somehow assess how reliable it is.
5. Write instructions, which are to be included on ZeroPhone Wiki.

The stakes are, undoubtedly, high, and rewards consist of some Latvian chocolate mailed to people that help the most =) Performance and compatibility tests with various Bluetooth devices (ideally, audio output devices and streaming music to them) and any other insights will be highly appreciated.

UPDATE: "The thread you linked works for a Rpi3, but not the Rpi0w." So, we need to dig deeper - there's some action going on in the linked thread.