Honestly, if you want to give the kids a premium experience for a discounted rate, I'd go with one of the Gulf carriers, or one of the Asian carriers.
Emirates, Etihad, Qatar, Singapore, Cathay Pacific, etc.
And a wildcard that would be budget friendly if you're not concerned with alcohol would be Saudia.
Emirates and Qantas are two airlines that invested heavily in the A380 so they'll have them in the fleet for a while.
It was a sad time in 2019 when I took my final 747 ride on Qantas from Perth to Sydney and then followed that up shortly thereafter with a ride from Melbourne to Sydney on a brand new 787. After the scamdemic, a lot of the big planes are gone, replaced by smaller and more fuel efficient 787s and A350s.
For my money, if it's 16 year old girls, I'd make them watch Crazy Rich Asians a few times and then take them on Singapore Airlines to Singapore and let them run loose for 3 days or so while you chill out in the Marina Bay Sands swimming pool. And if you're a Call of Duty player, I'd play the MWII level with the Supertrees in Singapore before going.
If you spend any time in Brisbane, the Breakfast Creek Hotel is a must.
Obviously there is a ton to do in Sydney and myself or bthotugigem05 (who lives there now) could give you some pointers.
While I'm thinking about it, during the years that my daughters were in College, flying them back to Australia during their winter and summer breaks, I would sometimes use a mixture of points and pay and break up the flights into different segments.
One of the tricks I discovered was that I could buy cheap fares between Sydney and Honolulu and then use points between HNL and IAH (for my daughter who went to A&M) or IAD (for my daughter who went to VMI).
And with dad being super cheap, I did make each of them do an RTW trip because it was the most economical.
- A&M daughter went Houston to Moscow (refuel stop) to Singapore to Sydney
- VMI daughter went Washington Dulles to Dubai to Sydney
Another time, I also leveraged routes from LAX to Tokyo enroute to Sydney.
- A&M daughter went LAX to Tokyo to Singapore to Sydney
- VMI daughter went Sydney to Tokyo Haneda, transferred to Tokyo Narita and then on to Washington Dulles. She did that at age 18 and I was on pins and needles about her making the connection in Tokyo.