Unfortunately on xONEx tickets, PPT is a dead end, and you can only get there from SCL. If you are only interested in visiting NZ then a return LHR-xHKG-AKL (in J) or LHR-xSYD-AKL (in F to SYD) would most likely be the cheapest. If not, some options are:

1. Do your routing as above, but on an xGLOB34 ticket. Pricing for the D and A products are roughly the same as for an xONE4, which makes it good value if you have some more inaccessible places like PPT in mind for your trip. This ticket gives you 34,000 miles to play with; since LHR-HKG-AKL-PPT-LAX-LHR comes in at just under 24,000 miles you could very easily add an additional European/Middle East trip to your ticket later in the year for just the cost of the taxes. Perhaps a long weekend in Dubai for you and your wife? (see caveat below)
2. If you are still keen on the xONEx idea, the only way to do something similar would be to go via South America. Something like LHR-HKG-AKL-xSCL-IPC-xSCL-LAX-LHR would work, although it is a long way round and would cost more than the xGLOB34 .. and of course you can only get to IPC, not PPT.

If you are not fussed about the idea of an additional European side trip then LHR is probably as good a place as any to start. If you are, you would be unable to start from LHR because of fare rules which only allow you to re-enter your country of origin once. Starting in FRA would allow, for example, FRA-HKG-AKL-PPT-LAX-LHR-DXB-LHR-FRA on an xGLOB34.