Take a closer look at the front stabilizer bar.
There are two metal pressed-on bushings that center the bar. The bushing on one end of my bar cracked - allowing the bar to slide slightly toward the opposite side of the car. There was just enough movement that a portion of the bar rubbed against the suspension, causing symptoms similar to your situation. The only visible sign of this was a shiny spot on the bar.
Since the metal bushings are part of the stabilizer bar, it would have required replacing the whole bar (which I didn't want to do). But a standard stainless steel hose clamp was more than enough to hold the bushing in place; no noise since then.