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You need to carefully check the possible expiry of your points. Miles conversion nearly always result in a loss of value. Not 100% sure but AMEX Membership Rewards can go to SPG then to various airlines.
Several airlines go from the Middle East to Australia non stop (Emirates, Qatar, Etihad). And many others via Asia. Remember SYD is not the only airport in Australia.
Both BA & Qantas have high fuel surcharges when using BA avios / QF points for award flights.
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