Charging woes

Most likely there regulator is sensing low voltage.
Low voltage for the regulator is less than 14 something.

My best guess based on what you've written is there is a voltage drop between alternator output and the regulator's sense terminal.
Continuity will not reveal a voltage drop.
Measuring with the electrical loads off will not reveal the voltage drops.
To determine the problem.
A. Charge the battery on a charger (I know you think you've overcharged it but if it really was charging at 15-16 Volts it may have got hot and will actually be undercharged. Without an ammeter on an isolted charge line the charge rate is unknown. The voltmeter only indicateds the potential. That's the trade off)

B. Run the engine and measure the voltage difference between the alternator output and the closest location you can access to the regulator's sense terminal. The field terminal connection (blue - ignition feed) will work or the ballast resistor connector if its still there. Leave them in place - Just back probe them.