A light fixture in a 3-way circuit stopped working.

I have (3) 14/2 feeds coming into the light fixture, which I assume to
be power, switch-1 and switch-2. I have not touched the 3-way
switches.

However I am getting only 60v on the power feed. I am getting 120v
when I check between 2 different feeds. When I flip one of the 3-way
switches, I get 30v on the power feed.

The wiring is 55 year old BX (armoured). I had some loss of insulation
on the feeds inside the box from the heat of the fixture. When I bent
the wires out of the box, it started to crumble off.

When I turn off the power and check the resistance of the switch feeds,
only 1 of them goes to 0 ohms when I flip the switch. The other always
appears open with infinite resistance.

I was hoping to avoid running new wiring, but it sounds like I might
have a short outside the light fixture box. Should I start by
replacing the 3-way switches?

Any other advice/recommendations appreciated.