I don't see why a CAI ticket would be a factor. I always have LAX-HKG in my Cairo issued tickets, and have nary a problem getting the flight. I use the christep method of open dated tickets, and have always gotten my first choice of flights from LAX-HKG.

The ONLY flight on which I had problems securing space on the RTW I finish this coming week was from MEL-CNS. I booked a seat in coach in order to travel the day I wanted, and on the day, was able to move to biz. (I had an AONEx ticket, but this flight only had 2 classes of service.)