Thanks for all the feedback. I caught a flight on Qantas a couople of days ago, asked the unbelievably nice counter agent for help, and she sent me back to the same customer service desk that I tried previously.. This time however, with a QF ticket in hand for the day, the exact same agent who wouldn't help me before changed all 4 of our tickets to the 10:10 flight. Couldn't have been easier and no change fees involved. United wouldn't guarantee us a later foight since we had an illegal connection- might have had to buy new tickets if we missed the connection. Anyhow, big relief!