We used EAP to bring our 2 cats back to the US when we left HK. No problems, in fact they were exceptional. The cats were on a different flight than we were due to layovers and EAP handled everything perfectly. In fact, their flight was cancelled and EAP took care of booking them on another flight, kept them overnight waiting for the flight, AND refunded me $100USD because the new flight was less expensive. Can't ask for better than that!
One word of advice...send them in separate bins not together. Everyone gets testy in close quarters on a long flight.
Good luck and have fun in HK. We miss it terribly.