According to Wikipedia and the VW service tech Jaime, this is what is wrong with my car:
I am glad that on first pass I do not have a problem with the notorious high-pressure fuel pump, seen above as the “high pressure piston pump”. When that thing goes, the entire fuel system goes with it: $10k and several weeks of work (but covered by warrantee).
Update: here’s is the thread started on the forums. We’ll see what the community has to say…