1982 Plymouth Gran Fury - 318 w/ 114 amp cop alt (NAPA rebuilt 1 year old) and voltage reg also 1 year old. I was driving yesterday morning on the highway with lowbeams on when suddenly they flashed bright and both went out. I switched on highbeams and immediately they both burned out as well. I pulled over and waited for dawn so I could continue driving - then drove to NAPA and got a new voltage reg. Now I'm reading 16V on the electrical system with the engine running. Is this too high? What gives?

Poor ground for reg, poor voltage siginal to regulator or not unlikely a bad reg.
16 at idle is too high, probably goes higher with some rpm, maybe 18.

The Plot Thickens...

OK I ran the (calibrated) multimeter on the car and revved it up to about 4K rpm and: the voltage DROPPED to 15V!

This does not make sense to me.

high(er) RPM may have increased the electrical demand & reduced the full fielded output from 16 to 15 or something changed a bit inside the alt (where I think the prob is). Might be a bad (new) reg and or the alt field circuit may have grounded at the right place to full field it (which might be the problem in the first place. Subbing in another alt from your stash or another vehicle (no one "on here" has just one) but as you know I believe the Leece Neville alt has a unique mounting

What Robert said. I would lean to a short in the alternator with the field on one end grounded and the other end going to 12 volts putting it max output all the time.
Put your meter on each field connection. One should be 12 volts. Leave it alone. The other should be low, 0 to 2 or three volts. Pull that wire off. That should kill the output of the alternator. If it does not, there is a short in the alternator and it needs to be replaced.
If that did not affect it, then it is in the regulator or the wiring. Since the wiring runs along the top of the engine, wires get baked and brittle. The insulation flakes off and you have a run away alternator. Or worse, 12 volts goes to ground with other issues so check there as well.
Let us know what you find.
Craig

Correct, pull the green field wire at the alt & if it is still charging then it is the alt & first do a visual on the brush/brush holder assy

The OP likely has the Leece-Neville alternator which wires the same as the Mopar single-field alternator.