Philippine Airlines is fine as a carrier, 4 star, trying to be 5 star but dont expect it yet.
I'm flying PAL MNL-HND this month and quite happy about it both fair-wise and the service I'm getting for it.
It will probably JFK-MNL via YVR and then to Japan.
Its known to be a full service carrier but with more affordable prices. Its market in the US is HNL, SFO, LAX, and JFK.
The bigger concern though is if your bike will get to Japan in one piece and if it will be worth it. If it's worth anything buy travel insurance for your bike, dont count on the airline to reimburse you for anything. Another tip, dont put any valuables in your check-in baggage. In general when flying via MNL its possible to have your bags slashed by the baggage handlers., doesnt happen often but does happen, its a ongoing problem of the airport.
Maybe the forum here has suggestions regarding bikes.