Well, it appears that my Arduinos are not changing the state of D24, which goes directly to E0-EN.
I checked that the 10k pullup resistor on the RAMPS (R16) is good. I retouched all the solder joints back to the Arduino. However, when I disconnected the Arduino itself, I see can see in isolation that D24 stays at 5V when the extruder is called to activate.
I guess this is a firmware issue, although I used the preconfigured firmware available on the Wanhao group. I will have to fight with it a while longer, I guess.