Well, false alarm apparently.
Package arrived today, and no additional fee had to be paid. It seems that the DHL representative that contacted me was mistaken about the customs fees, and the big delay was caused by the fact that DHL needed confirmation that I am an individual and not a corporation.
EDIT: After checking the package, I can understand why DHL was in doubt whether I was a private person or not. While the packaging, if somewhat excessive, is still reasonable, there was so much legalese documentation included... One full page document for each position, and I ordered about 50 types of various SMD passives.
It is very obvious that hobbyists are not the primary marked for Arrow
The funniest thing though, is that everything, even the SMD resistors, is packed in an ESD bag (some components are even double packed), but the Raspberry Pi is just in carton box, without any (visible) ESD protection at all.