Unfortunately, the OP will not be dealing with the same agent that granted your request; rather than dealing with CI check-in staff at TPE, they will be dealing with generic third-party agency staff at SYD so will be highly unlikely to get the same answer.

Checkthrough is only guaranteed for flights all on the same ticket; you have no entitlement to it when travelling on separate tickets, even where it's technically and physically possible for a check-in agent to override the system.