Some thoughts for you

If you change either the LIM-LAX or the DEN-LHR to be on the AA codeshare, then AA will ticket for you

I suggest you fly CX on LHR-HKG, to avoid BA's rapacious fuel fine

Of course you could start from Paris - CDG-HKG on CX, unless you particularly want to go to London
That would also free up a segment, which you could use for your HKG-AKL-SYD (though I would suggest HKG-AKL-MEL-HBA-SYD-NOU)

You currently have 3 flight segments in SWP - SYD-HBA-SYD-NOU; your surface segment NOU-PPT does not count towards your allowed 4 free flight segments in the continent

Also, instead of DEN-LHR-TLS, you could fly DEN-DFW-CDG or DEN-ORD-CDG - if you wanted an additional stop in the USA

Mileage Monkey is good tool to play around with itineraries - http://www.slfft.org/mm