How do we organise an airport / train station transfer at the end of our stay in the house?

The transfer to the airport (in Tokyo Haneda or Narita, and Kyoto Kansai Airport) can be made in a shared taxi or by train.

The taxi-minibus has a tendency to allow a large safety margin due to possible traffic jams. It has the advantage of coming to get you from home. It has to be booked at the latest 3 days in advance.
With the train there are no traffic jams so it is dependable. But it is a bit more expensive (you have to get a taxi or the bus to the train station) and requires a little physical effort to reach the train in the station.