Having seen no reaction from the extruder motor, I decided to use the oscilloscope in FabLab to see if the correct signals were being sent. This turned out to be a more difficult task than expected, mainly because I don't have the first clue about oscilloscopes. I and a few other FabLab members fiddled for a while with the knobs and dials without seeing any output. The calibration output showed a nice signal, but nothing from the Arduino.
It wasn't until a 70-year-old electrical engineer offered his advice that we figured out what was going on: The signal was so weak that it didn't trigger at the voltage we expected. Even though the signal is supposed to be 5V, a capacitor somewhere in the circuit cut it down so quickly that we needed to go down into 1/100ths of a volt to see the signal. Must be something in the Arduino.
With this new knowledge, I ran raw GCode commands against the Teacup firmware. Trying the various extruder-specific commands didn't do anything, but just using G1 Enn to tell the extruder to move gave the expected signal. So it does work, if you just ask it the right way. I wonder if ReplicatorG doesn't do that. Looking at the generated GCode, it does indeed use the G1 commands, maybe it's just the manual control panel that doesn't.