Last night, I tried about 15 different numbers (including the one taped to the card and the new account line) and all led to phone agents who either couldn't transfer me or led to a dead end.
This morning, I finally got the card activated by calling the international global assist line and getting transferred to a couple different customer service reps - finally to one who knew how to activate a new card.
Of course, this begs the philosophical question: "How much will you let a business disrespect you just to get a juicy reward?"