Can I fly from Australia to Panama City without going via Los Angeles?

Q. As part of a round-the-world itinerary I want to fly from Australia – ideally Melbourne, otherwise Sydney – to Panama City. All the online solutions I am being offered seem to force me to travel via Los Angeles, which I do not particularly want to visit again. I am also keen to spend as little time in a plane as possible, and also to have a light carbon footprint. Can you offer any other options?

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