Does the rotor come up with acceptable resistance readings, according to the FSM? The FSM is available for download from the Home Page of this site. The FSM also gives test methods for the Rectifier/Regulator circuits, as well.
It sounds like your rotor is putting out AC, but maybe not enough voltage, since you only get 13.4 Volts on the battery posts, when revving the engine (above 2,000 RPM, I trust?...). If the alternator is not pumping out enough amperage/voltage, then the battery will drain, and die. I assume this is the problem?
Check the resistance readings for the alternator, and the Rectifier/Regulator, against the FSM, and you should know which direction to go. Best of luck! Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII