The most obvious routing would be of course on AA from PHX-DFW-KIX and would seem to be considered anywhere from "decent" to "very good" from most people on here. Also options include doing PHX-DFW-LAX on AA and then JL LAX-KIX or CX from LAX-HKG-KIX. With the option of routing through LAX via DFW would require an overnight in DFW or LAX because the JL flight from LAX-KIX leaves at 12:30pm (according to teh schedules I saw) and the earliest flight I could find that got into LAX leaving PHX via DFW the same day would arrive LAX at 12:10pm. This of course doesn't give you enough time and so you need to spend the night in dFW and take an earlier morning flight or in LAX.