Thank you sir. That has completed the lesson!

And, for the benefit of other readers I found Estel's advice based on his being a "fanatic of accurate measurement" when charging - also useful when discharging to ensure the EDV1 value changes before shutdown. Turn GSM off, close all apps, run bq27200 5 in terminal and (this is the twist) if you need to use a bit more charge to get you down to 3248 mV up the screen brightness for a few seconds and then drop it back down to minimum, monitoring the battery charge with the bq27200 5. I found it extremely easy to get the desired 15 second result without bme getting in the way.