My suggestions - I have researched a lot ) It's nearly impossible task since Cathy/etihad is no viable option any more ! We are going this year in December ( 19 dec from DC to Auckland and returning back on Jan 1 )

I had all miles ( AA , Chase , amex and cap one, Citi ) and had all options to transfer. I started looking in dec 2023 when award opened . We are two families each of 4 .

this is my what I did and your best bet is this if you are lucky

1. USA to Singapore either direct or via Europe ) - Book using Aeroplan points from Singapore to auckalnd/mel/Sydney when schedule opens up - since you book on flexible rates you can add more flight later on and keep flexible rate till end.
Then add ,nyc to Singapore at flexible rates ( either direct or via Frankfurt ) - usually 48 hours later - very short window - each flight usually has 4 seats.
If you cant find nyc to Singapore then book ( LHR/Paris/rome/frankfurt/zurich to Singapore ) at flexible points.

when united/luftansa/ Swiss opens their schedule , add IAD/jfk/ord to Europe where ever ( LHR/CDG/FCO/ZRH/Frankfurt) you booked your flight to Singapore ( most likely economy but these tend to open bossiness as schedule get closer and December you will most likely get business closer to departure .

likewise return in opposite direction

If you are lucky you can find lax/sfo to nan and then to Auckland using Alaska or AA. I did not see any flight

Forget to find saver award on AA and united ( and 5 seats - climbing on mount Everest might be easier )

I did book this way for one way to use to Nz ( 8 seats with 2 family ) but ended up cancelling all since we booked star airlines RTW ticket startng from AMS ( this summer ) and returning back to AMS next year in 4500 USD ( two business trip - one to NZ and one to Europe )

Good luck