Well thank goodness - this damn washing machine was really starting to bug me.
Some basic troubleshooting led me to believe that the drain pump was the problem, but I didn't have a way of confirming that. I pulled the pump out and went to a Harbor Freight to pick up a multimeter. I checked for continuity, certain that it was an open loop.... and it wasn't. It was showing resistance.
Went back, connected the electrical leads without reinstalling (so that I could see the impeller), fired up the washer and... ******g pump starts spinning. Damn. It's good, so I've gotta look elsewhere.
Check all of the hoses for a clog - nothing. Did I miss some debris when I was taking it apart? Maybe. Put it all back together. Fill it. Drain it. Nope, still not draining.
Since I can't think of anything better to do, I decide to remove the pump again, while leaving the electrical leads attached... so that I can start a cycle and stick something in the spinning impeller.
Turns out that the slightest touch stops the impeller dead in its tracks - it's a bad pump after all! It's a bad pump after all! It's a bad pump after all - it's a bad, bad pump.