Any other suggestions?
We've looked at CUN-JFK-YVR-HKG-NRT on CX, but CUN-JFK (AA) arrives only an hour before JFK-YVR and the same with YVR-HKN (with only 1 flight a day we have to spend a day in NY and a day in Vancouver, which is a bit of a waste).

Basically we want to get from CUN (or SJU or BDA) to Tokyo on first without using AA.
JAL would be the obvious answer, but somehow F is not available on the RTW ticket!? I've even tried alternative dates randomly (and far into the future) and are getting the same response from travel agents...