The door panel comes off with 3 or 4 screws, and to get the regulator out, I used this tutorial:
http://www.delicaclub.com/viewtopic.php?p=169885#169885
After that, the motor comes off from the regulator with 3 screws, and the cap can be pried off with a screwdriver, leaving you with this:

Some investigation showed that the rubber had separated from the smaller gear that actuates the window mechanism. The red line points to the separated area. It's not necessarily a bad design, but it definitely failed at the weakest point.
To fix, I ground a slot through the rubber and the small gear, and I cut a chamfer in the rubber around the small gear using an exacto knife:

To transfer the torque better, I put a piece of tubing into the slot (brake line tubing that I had in the garage, you could use a bolt, a nail, whatever you have kicking around).

Then JB-welded the whole thing:

My theory is that the JB weld only needs to hold the tube to the back of the gear. The tube itself should transfer the torque from the rubber to the gear. Any torque transfer that occurs via the JB weld in the chamfer is just bonus. Looking back on it, I probably should have just tack-welded the tube onto the back of the gear. That'll be plan B if this fails.