IMO your voltage measure @2000 rpm with full load is an excellent test. This represents "normal operation", and the alternator output voltage should be where glmoy suggested - 13.2 to 14.1 volts.
The 12.57 volts you measured actually represents a discharging condition (if your battery was fully charged).
I'd feel comfortable with a decision to repair/replace the alternator.
2001 e320 wagon
2006 Crown Vic