I've updated the schematics – the commit log on GitHub should give a fairly good summary of the changes. The most important changes are adding a speaker (for continuity checks), a reset IC (to shut it down if the battery voltage is too low), changed the battery charger IC to one that can check the battery's thermistor, and made it so I can monitor the battery voltage.
With regards to monitoring the battery voltage, I've done that simply with a voltage divider feeding the ADC. My voltage divider divides by two with 1 M resistors, so that gives a current of ~2 uA depending on battery voltage. The maximum source resistance of the ADC is stated as 50 k, so I'm definitely not going to get an accurate reading of the actual voltage. I'm not concerned, because I'm only interested in knowing the battery state of charge – and I'm sure I'll be able to determine that just fine.
The PCB layout is progressing nicely.
The case design will be changing slightly from the graphic I've got right now, and I should update that soon too.