I've read a few things about using charging circuits and battery fuel gauges but it's a bit beyond what I know how to do right now. I might look in to it more in the future, or maybe someone else who knows more than me can add a fuel gauge to the schematic :)

I've used this which was very easy to get to work and there is C code out there to use with it. https://www.sparkfun.com/products/10617

Hmm, it seems like all the fuel gauges I can find are designed to be incorporated in to a bms, instead of being added to the input/output of an already existing bms. Do you know if there's a fuel gauge that can work with 12v so I can just add it to the circuit I'm using?

Could you measure a calibration discharge curve with a (digital) bench power supply draining constant current (or constant power) and use it as a LUT?

That would probably work. That's how I was originally planning on doing it, but I got annoyed with the voltage logging not working properly when I set it up so I gave up and just went with the linear voltage -> capacity reading. A potential problem with this is that every battery pack would be different, and people who make this project on their own would need to generate a table for their pack.

Not as simple. Voltage also changes with load and temperature for multiple reasons. You'd also need to account for that.