Just had a call from the NSW Health Services. They said that false negatives are common, but false positives are not. The doctor was great in outlining my options. He does not recommend I take a PCR. He says that if I quarantine and do not develop worse symptoms, they will provide a letter stating I can travel after completing the seven days. The US requires either a negative test or a letter from an appropriate health authority, so at least that give me a timeframe for flying home. He thinks I should go on antivirals and is looking into getting them for me.