After the phone-death that I captured above, I charged the device to 100%, and then left it to drain until death again. It lasted about two days with very light use, dying when it reported 10%, again with zero warning other than the ~15% low battery indication. I know that deep-cycling these batteries isn't healthy for them, but it seems to me that the cycle helped a bit.
However, I do still feel concern about the reported full-charge voltage, ~4.3 volts. Does such a voltage not severely reduce the number of cycles the battery can go through in its lifetime? Also, what is supposed to be the cutoff voltage for this battery chemistry? I thought it could go down to ~3.0 volts? My phone seems to be cutting off at a reported 3.5 volts.
That, and my perpetual-suiciding problem. Though, I'm about to encounter a change of scenery that will take me downtown, so I'll hold off on complaining more about that until I see whether or not the signal strength influences that.