Your itinerary would be okay with one caveat - you'd have to connect at JFK and not stop over there, hence ARN-LHR-HKG-BKK-HKG-SFO-MIA-CCS-xJFK-LHR-ARN.

One alternative you might look at would be using the North America flight allotment (6 segments) to get you as close as possible to CCS without leaving "North America" and then fly on a separate ticket from there, e.g. ...SFO-MIA-SJU-CCS-SJU-JFK... so as to save the ~US$1000 for the 4th continent.

Many people these days are thinking that service on QF is becoming the equal of CX on premium longhauls, but it's a personal thing.

As for miles earning and redemption, you need to look carefully at your flying patterns and at the individual FF plans' "earn/burn" ratios. A business or first class RTW can provide a rich harvest in miles and/or status, but the miles/status will only help you if it supports your own travel and flying plans and preferences.