If your alt is still pushing 16V then your battery should be charged if not overcharged.
Whats the volts at the battery with the engine off?
If its under 12 then you probably have a dead cell in the battery.
This is an odd one.
The regulator should have corrected the problem.
I have also seen new regulators that were bad.
Do you know any one with a known good regulator you can try to rule out that possibility?
When my regulator went in my 71 it pegged my amp meter, by the time I got it in the driveway the battery was swollen and oozing out acid.
That was a close one
Denny