I have had plenty of lost luggage, and I have never heard of having to make a personal phone call. In fact, when we were on our Norway cruise, BA lost all our luggage. I got to go in the lost luggage are at CPH, and it is huge! Size of a gym, and full of lost luggage.
Fortunately for us, we had a couple of days precruise in CPH, or we would have been in your shoes.
Hope everything else goes wonderfully!