According to :

For good measure, I took my DMM and measured AC volts between
another circuit's hot side (from the extension cord) to the K&T
neutral. 120 V, fine. Then I measured between the cord's hot to the
K&T hot. 120V? Wha? I rechecked with a neon lamp. The lamp
lit. The NM conductors, which ran through two 3-way switches
to another light fixture, which was off, read 79v each. Wha?

I don't get it. The circuit is definitely dead. I have accounted for
all the
other branches, some of which are multiwire, but this one is not.
Everything is turned off, and indeed there seems to be no DC path to
ground through the K&T hot, and certainly not through the disconnected
run to the 3-way switched fixture!

In K&T, inductive/capacitive coupling is a smaller effect than in Romex
because of conductor spacing.

If I've followed your scenario correctly, the 79v DMM readings could
well be inductive/EM coupling. "not zero and not 120V" is more
indicative of that than zero or 120V. One way to check out the 79v
readings is to turn the lights _on_. If I read your posting right,
the lights are downstream of the unpowered K&T section. The lights
shouldn't light when you switch 'em on, and the voltage will drop
to 0v (presuming the light's neutral is still connected).

You're measuring from the cord hot to the dead circuit's hot?
Is the dead circuit's hot touching anything grounded, including
the neutral, including going through any switched on device like
a light bulb? That'd explain it. The circuit _is_ dead, the hot
wire is acting as a neutral to the cord's hot.

Testing against an adjacent hot circuit just makes things confusing.

Neon testers don't take much current (touch one lead to a hot wire, hold
the other one in your hand, the bulb will light up even if you're
totally insulated, and you won't feel a thing).

But I really don't expect a neon to light up from _just_
inductive coupling to a disconnected wire.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.