Pimoroni provides the clean_shutdown software on Github for the Zero LiPO. The PIN used for the low power detection is configurable (trigger_pin).
Would you see any problem in using this software for the PiZ-Up Time hardware, using GPIO 26 as the trigger?
About the battery: Most 14500 batteries have a built-in protection circuit, which makes the battery about 2-3mm longer. Even the ones shown on the PiZ-Up Time product pictures seem to have this circuit built in.
I can fit such a battery into the holder, but the entire holder then bends upwards a bit, and the ends bend out. Is it safe to use such a battery?