I think the FAQ Sticky is out of date with regard to the restriction on the CX HKG-HAN flight.
There is no longer any mention of this restriction in the fare rules
And I have just constructed an itinerary in the on-line tool that includes the flight (using the KA designation; KA operates the flight and CX codeshares on it); availability seemed low, even if booking a business class itinerary

An option is to get to HAN via NRT (or to leave HAN via NRT); JL has a daily flight