I don't know much about family pooling, but I am assuming it works on partner airlines as well?
If so, I find Singapore Airlines has the cheapest 'flexible' fares ex-Australia. It is 120 SC round-trip per person from MEL/SYD/BNE to Singapore, which would be enough to get you what you need. It won't get you the four sectors though, unless you fly a VA codeshare (which IME does not get you the flexible fare SC). You might be able to fly a VA codeshare yourself and have the family on SQ flexi-fares, which would still be enough if you flew to BKK via SIN for example.
The cheapest SC seem to be flying W fares in DL in the USA, or sometimes even F fares. But you would have to get to the USA first.