The battery starts at about 4.2V fully charged and crapped out at some point just below 3.5V I think. I took a voltmeter to it about once an hour and with the 8.5 hour battery life I got, it dropped close to 0.1V per hour. Assuming it stays that way until the battery has been charged/discharged many, many times, it is a fairly linear scale. I was actually surprised to see this result, but it works out so well for what we want to do here if it is consistent for every cell
That sounds kind of weird. All the Li-ion cells I've seen drop quickly to 3.7 V and stay mostly flat before a rapid drop at the end of its life. Though... I've only looked at larger cells that one might incorporate in electric vehicle designs.
A coulomb counter would be more accurate for determining the remaining charge, but if the discharge curve really is almost linear, that certainly is convenient...
None of the li-ion batteries I've ever dealt with have a linear discharge. It's usually almost linear, dropping very little until it hits the "knee" of the curve, at which point the voltage drops sharply. From what MWeston is saying, sounds like that's exactly what happens, with 3.5V being the cutoff. Optimal operating voltage is probably around 3.8 volts.
Li-ion don't like to be overly discharged. Hitting 3.5V often will cause severe damage and can reduce battery life drastically.
Even if you take care of it, over time the battery will lose it's chargeability, but it shouldn't affect the max and min voltages. If you label 4.2V as 100% and 3.5V as 0%, and just do a linear scale between the two, that should be close enough. For best results, keep it stored at around 40%, and don't let it fall below 20%.