Hi Mr. Maisey - perhaps you want to try transiting via Singapore? Scoot offers a daily Singapore-YIA flight and there's plenty of flights between SYD and SIN. It's overnight with the transit but overall it can be a ~13h or so travel duration to Yogya. It's not a full-service though, so will not be as comfortable as Garuda.
Indeed the new airport is further away from city centre (1-1.5h drive), but there's airport shuttle trains that will get you to the Tugu Station in 40 minutes and from that station there are plenty of trains of all classes to Solo (typically takes 45mins - 1h). Of course getting a car and a driver would be more comfortable (albeit longer travel) - it'll probably be a 3 hour drive to Solo.
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