The early morning flight presents much inconvenience. You would have to stay at a hotel near Haneda Airport where you can catch free hotel shuttle service (please check hotel shuttle schedule). Of course, day flight means you can maximise your enjoyment if this is what you prefer.
The other option night flight is a slightly better choice in comparison. You don't have the hassle of getting to the airport early. Downside is inflight would be supper service & lights will be dimmed for sleeping. Breakfast serves before landing. Of course, champagne is served at your request.
Either way, they are not good choices in your case. Try the NRT option if you can.