So I'm guessing not a lot of speaker repair experts in these parts!
Anyway, here's an update and a warning for fellow JBL fans. Thanks to some helpful dudes on the Lansing Heritage forums, I got it figured out that bad lead wires on the cone near the dust cap were the likely culprit. Local JBL repair only wanted to recone ($264!). After much searching I found a local guy to look at it. He determined it was the lead wires and I paid him $30 to fix it. He wanted to give the money back--I insisted he keep it as a token of goodwill--because he doesn't think his fix will last. Why?
Because the turd I bought the speaker from on ebay had apparently already done a prior fix, done a decent job of covering it up so I didn't notice. But when my guy got me to see how there was a larger, odd solder blob (which kind of ruined the lead wire and makes further repair almost impossible) on one of the leads that doesn't match any unmolested K120, I knew I'd been taken by an ebay scoundrel. Predictably, this douche sold it as all original, blah blah. Also, even though he only lives a few miles from me he wouldn't agree to local pickup (even at a neutral destination); I knew something was stinky right there.
Live and learn, I guess. But if you're not already being careful with ebay JBLs, I suggest you always take a really, really hard look. That's my PSA for the day. These bad boys are getting up there in age and there'll probably be more and more inscrutable folks out there trying to offload their questionable goods for top dollar...especially knowing what it costs for JBL recone kits these days.