Well, it came back.

I installed a brand new connector, and it came back again. I did a little more experimenting, and when I shut off the Alpine's internal amp, the hissing stops. So it's some kind of interference from the internal amp, affecting just the left rear speaker.
Sooooo, that (in addition to the fact that my old Kenwood is acting up) was all the ammo I needed to convince my wife I need a new amp. I found a deal on ebay for an Alpine 40W x 4 ($91 + shipping), so I'll run all 4 speakers from it. Hopefully that'll solve it for good.
Now if I can figure a way to send the signal to the sub's internal amp, I can shut off the head unit amp completely. Is there a way to convert pre-out to speaker-level input?
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Jeff - '01 Inferno Red 27G, w/ABS, 3-ball shift knob (homemade), passenger armrest, Passport 7500, lowered, painted bumpers, various chrome bits, Alpine w/iPod control, Boston, OEM sub, MA reg. PTEEEE