I ended up doing a complete reinstall from scratch to upgrade Zoe to my new Pi-Zero-W, so here’s my latest set of installation instructions. I recommend printing these off so you can refer to them easily as you do the installation.
These work for any version of Raspberry Pi running the latest Raspian Jessie Lite.
I can confirm that the Pi-Zero-W inbuilt WiFi does support WAP / soft-AP.
Annoyingly, I messed up soldering the GPIO connection onto the Pi-Zero-W, so I have another one on the way.