There are several reports that everyone headed to HK on the CX flight from JFK this week -- over a 100 people -- were denied boarding because their health documents were not in order. The requirement for some sort of government document certifying the authority of the lab which took the test is not practically available in the U.S. Nor are lab results with your passport number printed on them.
All the Government/CX will tell you are the required documents. The don't tell HOW to get them, which is the critical problem.
So reports in this thread from travellers who know first-hand what works and what doesn't work and where to get the paperwork done would be very valuable.
I also saw reports that everyone (or practically everyone) on this morning's flight from LAX were denied boarding due to insufficient paperwork.