I was investigating booking a Melbourne to New York return flight on this deal: https://www.ozbargain.com.au/node/503209 when I saw there was also a United Airlines flight option around the same price for some of my test dates. Given that I had the United AmEx offer from this deal: https://www.ozbargain.com.au/node/483908 saved, that seemed better value. I then noticed that United offers free stopovers, so turned my New York-only trip into LA (a week), New York (two weeks) and San Francisco (just under a week), all for $806pp after the cashback. Seems great value for my first trip to the US. Note you can book for up to 6 people on the AmEx offer, and so long as each person's flight total cost is over $1000 you get the $200 cash back per person.
My dates are 1 May MEL-LAX, 8 May LAX-EWR, 24 May EWR-SFO and 30 May SFO-MEL. All flights are direct. There was only one flight per day to-from AU, but there were several options to choose from between LA-NY and NY-SF at the same total $1007 ticket price. Sorry I don't have time to check if this works from other cities or on different dates, but given that some of the Qantas options from the first linked deal were UA codeshare, those dates seem a good place to start - I haven't seen this United fare advertised anywhere as a special but there seemed to be quite a bit of availability on the dates I tried). Flights are full service (if not awesomely reviewed) with baggage allowance of 2 x 23kg per person.
Hoping this is of benefit to others, especially if you have the United Airlines AmEx offer saved.