67 Barracuda Heavy Electric Load

You should try a known good battery and see if it's that. It just doesn't sound like the alt. JMO
Not to muddy the water but you could convert to Denso. Read up on it there are a lot of threads here.
Denso alternator upgrade
1991 TOYOTA 4RUNNER 2.4L L4 Alternator / Generator | RockAuto