I feel like the advice I'm getting is that the schedule has to be relaxed. The LST commitment is fixed, but maybe I can move the ROC one and fly LST-MEL at 1645 on QF, then connect onwards via SYD-NRT/LAX-ORD. Thanks for the warnings.

I'm still curious, though - if there isn't protection from misconnects, what benefit (other than a free snack and drink, and the ability to earn QF points on the highest fares and to redeem QF points) is there to booking the QF code on the JQ flights? Is it just there to simplify the rules on through QF international fares with AU domestic connections (eg 'book on QF flight numbers only')? If JQ is an LCC, why not call it one and not have QF-coded flights on it?