Just to let anyone interested know that I worked out how to book the taxi in advance in the end. I successfully booked taxis to and from the airport, and had a great weekend with DS in Antwerp in between! The taxi arrived promptly both times. The taxi-driver today was a very chatty and funny Romanian chap who spoke perfect English, and dispelled my preconceived opinion of Romanian immigrants.
Passports not in the drawer I always keep them in. Turning the place upside down.