If you want to include NZ then I suggest you take advantage of the exchange rate and start the RTW there. That way when you get back to OZ you still have a one-way flight to AKL up your sleeve for another visit, or to start another trip.

As a sample itin it would look like

SYD-AKL separate ticket on LA
AKL-HKG-SIN-HKG-FRA//LHR-LAX-SJU-JFK-BDA-MIA-DFW-JFK-SYD-PER-ADL-AKL

There is still 1 more SWP segment (eg if you wanted you could start AKL-SYD-HKG with stopover in SYD but then there could only be 1 more stopover at the end) and assuming you use the available extra SWP flight you also have 4 more flights which can be used in asia (up to 2) and europe (up to 4).

By having europe to NA flight into LAX you get much more miles and status credits.