With a new pair of gears from Thomas, I put the extruder back together again. It took a fair amount of sanding and Dremelling to get the bits to fit, but eventually they did. The screws holding the hotend are rather bent, and not able to reach the holes on the other side:
Getting the extruder onto the X carriage was also quite fiddly, worse than before because this extruder mount is lower and so there's less space below the motor. Not sure why it's so important to have it be as low as at all possible. Once this works, I may just redesign it to be a bit higher and print a replacement. See that little space under the motor? I got a washer and nut in there to meet up with a bolt. Not simple.
At the same time, I've moved from my previous Linux laptop (which, alas, was driving me nuts in a number of ways) to a Mac (which merely confuses my Ctrl/Alt muscle memory). I made a copy of my home directory with all the Arduino stuff, but it wasn't quite enough to get the Arduino program to accept the Sanguino board just yet. Grrr.