I picked up a spare insulator spacer from the MakerBot store, and replaced the plastic insulator in the extruder nozzle with the new piece. This time, I again had problems getting the extruder started. After a couple jams, I tried using a tiny drill to unclog the nozzle with no luck. What did work was removing the old plastic filament, cutting it flush, putting in a new one, and trying again. After a couple rounds of this, the extruder started working perfectly! You can see the two piles of extruded plastic. The left one got formed by raising the Z platform as the plastic pile got larger. The second was made by moving the X and Y table as the plastic extruded.
My suspicion is that I had some debris clogging the nozzle. Backing out the plastic rod and cutting off the stretched end eventually got rid of the debris.
I was having good luck extruding at 215 degrees C. Heating it higher didn't appear to change how things worked.
It's too late to try running a noisy print job - guess it'll be tomorrow or the next night.