Both AA and BA are on one-way system. A R/T essentially is 2 x One-Ways. AA does not allow Stopover en route. BA essentially is charged by both distance and segment, so technically you can book 1 ticket for each segment needed, essentially give you a stopover at HKG.

One-way on AA is 55K each so you barely have enough miles for 4 one-way Js using your AA miles.

BA is not zone based program since Nov 2011. It is now a distance + segment based program. There is no way to know how much you need until you give a specific itinerary. The cost varies GREATLY based on how you fly, not to mention the $300 or more fuel surcharge on EACH ticket.

AS is a round trip program for partner award and it is 120K to Asia on CX per award. It allows a stopover en route. This is the only program that allows you to have a stopover at HKG.

In other words with your current stash, you would need to split your booking across all 3 programs, and no stopover other than the ticket booked with AS miles.

One person goes on AS, other persons go on AA one-way and BA one-way but you dont have enough BA Avios even not thinking about the fuel surcharge.

You may not even have enough BA Avios for 2 one-way tickets to PVG if you are from East Coast or you need a connection to go to CX gateway. Besides, since CX has to connect at HKG from JFK in order to get to PVG, BA award would be JFK-HKG one price, then add HKG-PVG another price, to get to a total Avios needed.

PS
Somehow I vaguely recall someone has asked very similar questions before.