If contemplating an AONEx, then also you should pay attention to which sectors actually offer F (remember DONEx books into A on 2-class N. American flights.)

For example on your initial itinerary, you'd only have international F between LAX and LHR, LHR and DXB, and and HKG-SYD. All other segments would be with J as the top cabin (except the AA flights within N. America.)

Yes, you can end anywhere in N. America. Note as of a couple of days ago, the 20-segment rule includes surface segments.