The end of this story:
I went to the library today and talked the librarian into halving the charge (down to $20). They still got to keep the book. I guess that’s fair, and I can live with that.
Thanks to all who supported me with kind words and advice!
I would also like to thank a nice lady librarian from another branch who unblocked my account the day before I actually paid the fine, because I had some books on hold and the hold was expiring. (Not a matter of life and death but I would have to order them all over again etc.)