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"Could someone clarify this:
Chase Sapphire Preferred and Chase Mileage Plus Explorer, irrespective of the rewards program (AA, MR, UR ...) of your trip, if you pay the taxes with any of this card, they will give travel insurance for your trip for no additional cost?"
Yes, they do. But for your situation, the insurance would be nearly worthless. It might only cover what you paid in cash for your AA awards. The coverage would be better for a trip delay caused by weather, flight cancellation, mis-connect, etc. You should be able to find the benefits guide for these cards via a Google search. And your no-fee Chase Sapphire card might provide some coverage too. My no-fee Chase Freedom card provides Trip Cancellation and Trip Interruption coverage, but not Trip Delay coverage. Note that credit-card coverage typically does not extend to pre-existing conditions.
With a little luck, if you must change the departure date of your SYD-SJC trip, you will be able to find award seats on the same carriers, and not incur any change fees.