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I think I'm going to be able to get around the DAC issue (thanks for the heads up).
Conceptually I don't understand how any battery can be charged without using some beafy diode to prevent current flowing out of the positive terminal (otherwise all what would happen would be similar to adding batteries in series) but still having a complete circuit so electricity will flow at all... I don't want to use a dedicated IC, I would like to build something myself and everything I'm finding on the internet is pointing me to these IC's...
user52526
@Gordon
What voltage are the high capacity batteries?
If they're the standard single cell (3.7v) ones I'd really consider just using a dedicated IC like the MAX1551/MAX1555 (in fact if you have a rev 1.4 original Espruino board, there are pads on the board where you can solder one). In reality it's probably cheaper/easier than getting a constant current and constant voltage source.
The issue is that Espruino's ADC and DAC only handle voltages between 0 and 3.3v. When reading voltages you can just use a potential divider to step the voltage down, but for the DAC things become a lot more complicated (it also can't supply much current - so it'd take a long time to charge a battery from it).
In terms of measuring condition, perhaps you could measure the battery voltage, and the current flowing into it (using a low value resistor between the charger's GND and battery's GND). You could then get a much better idea of how much power was going into the battery.