Battery voltage drop

Those readings sound pretty darned good; looks like it is fixed! The slightly lower 13.9V charging voltage at the battery when it is warmed up is normal; alternator voltages normally drop a bit hot versus cold. The much lower field voltage says that the battery is taking very little charging current, so is well charged.

12.5v for the battery off is a tiny bit low; I would take some readings on sevaral consecutive mornings to see if it holds at that voltage. And, your meter could be 0.1v low. If you want a poor-man's meter calibration, check the voltage on an unused 9V transistor battery new out of the pack; it should read 9.6v or 9.7v.

Congrats!