So, I went through Jur's list, point for point. And I think I've finally solved it
The bearings on the front suspension pivot were dirty with a black powdery substance. I think the fork may have a slight manufacturing defect, because the alignment of the bearings was a little off - this may have caused the rubbing. On one side the bearing just slipped out. On the other, I had to twist and wiggle the fork because both sides of the pivot were not aligned 100%. Not far out, but not quite right.
Anyway, I cleaned them up and packed them with grease before reassembly. I did a quick test ride, and it was smooth and quiet. Joy! I'm going for a 40 mile ride tomorrow, so that would be the final proof... I'm hoping for the best!
[EDIT]: to anyone who has a creaky Birdy and wants to grease their pivots - note that the manual states when reassembling you must use thread locking compound to hold the two halves of the pivot bolt together.