Actually, having taken the limo bus (my apartment was right across the street from the ANA Hotel in Akasaka), I would never take the train to the airport again unless I was picking up/meeting someone there. It was about the same cost with only 10% of the hassle (which was dragging my luggage across the street).

In fact, I'd go as far as to say that you should just avoid attempting the train at all on Tuesday and just go with the bus. Or, as someotherguy said, stay in Narita (it's actually supposed to be a nice town).