I've tried running the disposal longer, with lots and lots of water running through it. I've also tried running the disposal while (carefully) using the sink spray-hose to try to wash down the sides of the disposal while running. No joy.
Water seems to drain fine through the sink, but I can't figure out why the food won't clear.
Is this a problem with the disposal, or is there likely some other underlying cause (clogged pipes, etc) that could be causing this?