In the 1st itinerary, you can't do the SYD-NOU as that is a QF codeshare, not QF metal. The mileage based Global Explorer does allow this routing.

In the 2nd itinerary, you have 2 entries into North America. One has to be a transit without stopover (less than 24 hours). As listed, that would have to be your 2nd entry into the USA. Not sure if the actual next segment has to be the transit or whether you can slip in a segment to get to the intercontinental departure before your 24 hours are up.