Let me just try (and hope that somebody will try to improve.....)

If you plan a 4 continent you could add either Australia or Africa or South America. I also assume you want to avoid AA F and focus on CX F, JL F, QF F and BA F.
TLV-LHR(BA)-HKG(CX)-HND(CX, one of the few flights in Asia with F)-HKG-BKK-HKG(CX with F on some flights)
-SYD(QF/380)-some segments in Australia-HKG(QF 380, direct connection)-ORD(CX F)-BOS(AA)-...segments in the US-LAX-LHR(BA)-TLV.