There is no reason to worry over a 4-night stopover in HKG. Route like this: JFK-HKG O/W, PVG-JFK O/W. You have enough AA miles to book this in your preferred cabin, so I would start searching for availability.

The BA miles will come in handy for the HKG-PVG leg, which you can redeem for a O/W award at what I think will be a good rate.

Flying CX to PVG is a little annoying. I flew this route a lot of times last year, and almost always I wished I'd connected in Narita instead. You might want to look at schedules and availability for JL also because when you connect in HKG, you are flying over PVG and then coming back north. It's not a biggie, but it is a little bit annoying.