One of the problems inherent with this project is how to go from a blank SD card to getting a Pi Zero on WiFi and running the clock code.
A quick google for customizing Raspbian images led me to PiBakery. This looks like the easiest way to get the job done.
To that end, I'm going to see if I can develop a PiBakery block to fetch, compile and start the clock daemon. If I can do that, then there's also a prospect for sharing a canned PiBakery configuration that will create an SD card to just do everything required and write an SD card in one step.