Why this pair is the hardest common one
Most transatlantic pairs have a civilized overlap. New York to London gives you 9 AM to noon Eastern against 2 to 5 PM in London. Even the US to India, which has no strict overlap either, at least offers a morning-for-evening trade both sides can live with. New York to Sydney is worse than both, because the gap is nearly a full half day: when New York sits down at 9 AM, Sydney is going to bed at midnight.
The math leaves exactly one family of solutions. New York's evening is Sydney's morning. There is no morning-for-morning option and no afternoon-for-afternoon option. Once you accept that, the scheduling problem gets simpler, because you are choosing within a narrow band instead of searching for an overlap that does not exist.
The shoulder-hours trade, season by season
From April to October, the gap is 14 hours and the window is kindest to Sydney: 6 to 8 PM in New York lands at 8 to 10 AM in Sydney, a normal start to the day. From November to March the gap stretches to 16 hours and the same New York slot lands at 10 AM to noon in Sydney, still perfectly civilized. The transition weeks in early October and late March sit at 15 hours, splitting the difference.
Notice who pays in every version: New York. The Sydney side never leaves working hours in the 6 to 8 PM New York slot. If your team meets weekly and New York permanently owns the evening, say so out loud and rotate something else in return, like letting New York pick the day, or alternating quarterly with a New York morning slot that puts Sydney on night duty instead. The rotation habit from the US-Europe guide applies here with more force, because the burden here is entirely one-sided by default.
Three habits that prevent the usual disasters
Write both times and both dates in every invite. A 7 PM Tuesday meeting in New York is a Wednesday meeting in Sydney. "Tuesday 7 PM ET / Wednesday 10 AM AEDT" leaves no room for the classic mistake of someone joining a day late. Calendar apps handle this if you set the time zone explicitly on the event, but the human-readable line in the invite body is what saves people.
Re-check the week you book, not the week you planned. The gap changes twice a year on each side, and the US and Australian transitions do not line up. A recurring meeting set in September will silently shift by an hour for one side in October and again in November. The planner on this site's homepage computes the overlap from the real time zone database for any date, which beats mental arithmetic.
Default to 45 minutes. An evening meeting that runs long is how 8 PM becomes 9:30 PM. For a slot that already asks New York to stay late, a hard stop is a kindness. Send the agenda in advance so the shoulder hour is used, not warmed up in.