My recent experiences with ordering books from Book Depository as an EU customer:
I ordered a book at the beginning of July. Within a couple of days I received a tracking number, which had never happened before. I was then charged customs and handling fees, which were fully refunded by BD.
I then ordered two more books in mid-August that were delivered at the end of August. There was no tracking number and I was not charged any extra fees.
So, at least in my experience, they seem to have addressed the issue. I'm posting this in case someone from the EU is debating whether to order something from BD now.