Where are you measuring the charge voltage? I wonder if you have bad grounds or voltage drops. Try measuring the voltage right at the battery terminal of the alternator. Engine running charge voltage at the Battery terminal at the alternator should be 14.6 volts or so, what ever voltage you have there you should have across the battery if not you have a voltage drop. With a pair of set of jumper cables attach one negative lead to battery negative terminal and the other negitive lead of the battery jumper cables to the engine block, does the charge voltage raise? If you want to check for voltage drop I saw a youtube video that was good. When you checked the diode pattern did you use an oscilloscope to check the diode pattern?
There are several ways to measure and test the battery and charging system. To test the charging system the battery needs to be fully charged. A fully charged battery will have 12.6 volts at rest, a 200 Amp load for 20 seconds should not drop the battery voltage below 9.8 volts or so and the battery should recover, That is a High rate discharge test. older batteries you could do a hydrometer test to check the state of charge by sampling the electrolite level in each cell of the battery. With the engine running the alternator will put out about 14.6 volts. The alternator produces alternating current, the voltage regulator limits the voltage to 14.7 volts or so and internally in the alternator ac current is converted to DC current.
The guy from AAA was using something that he attached to the battery and then printed out a slip of paper that showed the diode patteren. Not sure if he did the othere things you mention. He did say that when he first attached to the battery, it was 14.5 then dropped to 13.4.