[jyl]

Just bringing "closure" to this.

The problem was many-fold. The old 1/2 HP disposal's underside flange was a mass of rust, the flange wasn't sealed right. I think water had penetrated the old disposal, causing a short that was tripping the GFCI more and more often. There was a plastic straw and something that looked horribly like mouse remains in the P-trap and a disgusting clog all the way to the Y-fitting.

Cleaned out the plumbing, replaced the disposal with a 3/4 HP model, replaced the flange using buckets of silicone caulk. All appears well. Thanks, guys.