Funnily enough, I’ve just been organising a European holiday that ends in Budapest! We’re taking a slightly different strategy to get home, which you might like to consider. We’re paying for a cheap Turkish Airlines flight to Istanbul in Economy (they fly from Budapest three times per day, and tickets can be as cheap as EUR87), staying overnight in Istanbul, and then flying home in Business class on Singapore Airlines from Istanbul for a bargain-basement 86,000 points each.
If you were to use points to fly all the way from Budapest, you’d probably fly Turkish to Istanbul, then either Turkish or Singapore to Singapore, and then Singapore Airlines to Sydney. It would cost you just under 120,000 points each. That’s why we decided that paying for a cheap Economy flight to Istanbul (Pegasus Air, a Turkish budget airline, flies from Budapest to Istanbul too) was worth it to save over 30,000 points each.
I’ve found that, for difficult-to-redeem Star Alliance redemptions via KrisFlyer, downloading and filling out a “Partner Airline Reservation Request” form is an efficient and relatively easy way to get things done. Email it to KrisFlyer and someone will call you within a day or two to (hopefully) confirm the booking. I wasn’t charged any extra to do it that way either.
All the best!