Thank you all for the assistance.

I think warbling is suitable in this case; one of the definitions is "to become sounded with trills, quavers, and rapid modulations in pitch", though you are right that it is predominately used to describe birds; I assume that is because they rapidly trill and modulate pitches while making their calls.

Definitions aside, I believe PFR is correct. I think mildew got in and over time the moisture expanded and contracted, resulting in the tape tensioning itself, making the tape brittle and creased over time.

I unspooled the tape a section at a time and ran the unspooled section through a fine cloth between my fingers. This removed the whiteness (at least, for now, I suppose) but didn't fix the distorted sound.

As for damaging the machine, I suppose you're right, though that 7 second or so clip was the extent of the playtime it saw and it hasn't seemed to affect playback on other tapes. Regardless, I've run a head cleaning cassette through a few times just to be sure.