Blowing Voltage Regulators

I think you're looking up the wrong tree.
You're battery feed seems pretty good. He has managed to run the car at night on battery juice a bunch of times.
The problem seems to be on the alternator or regulation feed.

You said the car works fine during daylight.

I am guessing that the alternator feed (the line carrying power created by the alternator), or the regulator feed may have a weak connection or bad insulation. When the current draw goes up, it either opens or jumps to ground.

What would be helpful to know is:
a. whether the ammeter was showing discharging or charging. and with just a little more load on it - like parking lights or heater fan what did it show at idle and above idle.
b. Exactly what failed inside the alternator or voltage regulator. The mechanical ones are pretty easy to see what failed.

Is the headlight relay drawing power from the alternator stud or a different location?
Does it have fuses or a breaker. (15 or 20 amps)?

Finally: Don't run the battery down and then use the alternator to recharge it. That is really hard on the charging system and the alternator.
Charging Battery with Alternator - Warning