I think if they can't get you onto the next flight in F they need to pay ANOTHER $800 each plus re-route you. Have a look around to see what you can do on other One-World carriers (on their dime) maybe HKG-NRT-JFK or HKG-PVG-US etc on AA.
A hotel is nice for the 12 hours. It's now time to get on with life and get to your destination with all deliberate speed.