I picked up a new serpentine belt (a Gatorback, the most highly recommended by the guys at crownvic.net) and installed it. Unfortunately, the light still comes on under hard acceleration. The chirping at upshifts is gone, however.
From what I've read, the brushes on these things are not separately replaceable, and I can't find anyplace that has separate brushes. That said, everything works just fine as long as I don't get the engine RPM up too high, so for the time being I'll just avoid hard acceleration. Even when the light comes on, nothing is affected. Lights don't dim, the engine doesn't slow, the voltage gauge stays within the normal operating range, etc.
Alternator replacement is probably the only real fix for this, and I'm not in the market to spend $220+ on a new one right now.