We have found flights via Honolulu, Hawaii are the cheapest via Jetstar. Return from HNL to MEL were US$600-700 in December 2024. There are also direct flights to Melbourne from San Francisco and Los Angeles. We would highly recommend spending more than 1 week in Australia, not only because there is plenty to see but because the flight is a real journey. It's ~15 hours of flight time direct and you cross the date line, so flying into Australia you will lose a day, but don't worry, flying back to USA you will gain the day back.
We are happy to organize transport for USA visitors from Melbourne to Mornington. Hiring a car in Melbourne is recommended and driving on the other side of the road isn't as scary as it sounds. James' family and friends have unknowingly graciously offered their spare seats to visitors. There is also a train you can take from Melbourne to Frankston and then a bus runs from Frankston to Rye - https://www.rome2rio.com/map/Melbourne/Rye-VIC-Australia#trips/transport/Melbourne/Rye-VIC-Australia/r/Train-bus