Personally I woud initially be trying to achieve a twenty four hour rail service to the airport now using existing lines and running a shuttle from the station that did not halt for three hours during the early hours. A lot of flights depart just after six am so a check-in two hours before would require arriving during this dead period, but as far as I am aware there is no rail service and if you do arrive at the station during this period you have to try and find the mythical bus that connects the two whilst essential maintenance is carried out or hoof it to the terminal with your bags.