While trying to remain below the 22K mileage limit, visit NZ, and follow the routing rules is a bit of a challenge when starting from Ohio. cmh-ord-lax-akl-syd-nrt-ord-cmh can be done. Reverse direction is ok as well. However, the syd-nrt is overnight in both directions and no skybeds on that route. cmh-ord-hnl-syd-akl-lax-ord-cmh has the hnl-syd during the day which is not as bad. Can one include HNL as meeting the requirement to route via the central/north pacific? I was not sure whether the fare required visiting Asia at some point on the routing.

Other notes: the only AKL-Asia on OW is to HKG which exceeds the mileage limit. My relatives who would be flying are limited in time and want to spend most of the time in NZ, not on airplanes. Intend to check Air New Zealand as a possibility as well.

Sorry, the rules require a "north pacific" crossing and HNL-SYD is "south pacific". So while it doesn't say Asia, it nets to requiring Asia in the routing. You can do HNL but have to return via HKG or NRT. At that point the OWE fares are better value over the 26K circle pacific.

Or start and finish in LAX and use miles or a cheap fare to get to/from LAX. Then do LAX-NRT-SYD-AKL-SYD-HNL-LAX.

Another option is to purchase SYD-AKL-SYD as a separate ticket. Such fares is cheap at the moment at there is string competition with EK dumping lots of capacity onto the market.