Using pandaperth's idea, you could also get a cheap return WLG-AKL and do something like:

akl-hkg-jfk-mia-sfo-lax-dfw-sea-lhr,lgw-krk-lgw,lhr-nrt-hkg-akl

where the first visit to HKG is a transit without stopover, and you have an additional sector left over to add in wherever is appropriate (or to finish with NRT-HKG-SYD-WLG I suppose). Another option might be to fly directly in and out of LGW; my first effort for this is:

akl-hkg-lax-sfo-dfw-mia-dfw-sea-jfk-lgw-krk-lgw-fco-nrt-hkg-akl

again with a sector to add in to taste. Note that MM says there is no JFK-LGW flight but the oneworld timetable says there is one daily. Also note that while JFK-LGW is not ideal for mileage-earning purposes compared to LAX-LHR, flying in and out of LGW gives you two extra sectors with which to make up this loss.