I'm having trouble working out the best way to do this...I'm trying to maximize tier point earning, whilst at the same time not sitting on planes all the time (i.e. I don't really want to be doing any more segments than shown below). The only destination in NA I actually need to get to is MIA. I picked LAX-JFK because it's served by a 3-class plane (i.e. I can make best use of the "A").

LHR-LAX-JFK-MIA-JFK-SYD

Is the JFK-SYD segment permitted, even though I've completed a trans-continental LAX-JFK? I.e. The QF flight JFK-SYD makes a stop at LAX, so this is technically a second transcontinental. Does that contravene rules or is it OK?

If it's not permitted, what's a good way to restructure this? I want to get to MIA fairly quickly, and could afford more segments on my way out. Also the LHR endpoint is fixed, but I could move the next continent to Asia - but only if I'm allowed to transit through there on my way to Australia - and then permit some further Asian stuff later (incl. NRT / HKG and then to LHR) is what I'm thinking at present).

Any thoughts & guidance?