Cathay Pacific although landed at Haneda Airport but the flight time darn long (11-18 hours long) with stopover at HK.
SQ got direct flight (6.5 hours) to Haneda but the cheapest price for 2 flying economy is $2017 compare to flying Delta also direct flight (6.5 hours) but to Narita at $1260 for 2 economy paxs. Early morning flight reach Nariita at lunch time, eat and board NEX for a 1.5 hours afternoon nap, reach Shinjuku, get off walk 3 minutes into the hotel. If take SQ reach Haneda already 11pm at night, after clear custom might need to take taxi to hotel; rush like mad dogs.
Any flight that last more than 4 hours, best to fly norm airlines instead of budget, more comfort.