70 + voltage regulator issue

Replaced the VR because of not charging the battery.

OK.
So we can figure out some of it.
I'm going to assume that when you installed the headlight relay harness, there were no other changes.
So I'm guessing you observed the 'alternator gage' showing the battery was discharging.

The low beam filiments broke (lights were only a month or so old).
I'm not sure what the fuse or breaker rating is that Rob included in the harness. But its certainly possible with a 20 amp or even a 15 amp fuse the low beams could burn out first.
It's definately possibile they were being supplied at too high a voltage.
This could because the alternator is producing at a higher voltage than the regulator is seeing.
In other words there is are voltage drops between the alternator output and the regulator sensing terminal.

Why do I suspect the VR caused the lights to blow: ON starting up after the new VR was installed the lights got really really bright then both went out.
Its possible, but in this case its just as likely that there is excessive resistance in the circuit.
The reason I say this is because the battery wasn't getting charged.
When the new regulator was installed, the battery was low on charge.
Here's what I think is happening:
The battery is low on charge. When it is offered power at 14ish Volts, its sucking over 25 amps. You can estimate the amount of current its drawing from the ammeter. The ammeter is scaled 40 amps charge to 40 amps discharge.

The differenec between say 30 amps and 5 amps is this -
Voltage is reduced when current flows through resistance. The more current flowing, the more the voltage drops. The regulator only sees the voltage after the resistance. All it knows is the voltage is low and increases the voltage of the alternator's output.

So thats one possible scenario.
Regardless put the battery on a slow charger.
My suggestion is to buy a cheap multimeter. It just needs to be good enough for you to measure voltage near the regulator and compare it to voltage out of the alternator and at the battery.
You wrote the voltage seems to follow rpm. If thats what you meant by pulsing, that narrows it down to not regulating or not getting the correct information to regulate. The multimeter will let you figure out which it is, and if its not getting correct information, you can further backprobe to narrow down where the major resistance is located.