Thanks for the comments, I am not allowed to stay for a night in LA apparently – but will get about 10 hours to look around the town. (possibly as I will be in NA before SA).
The miles is a great pint, I am unsure of the situation though with who/what to do about joining a frequent flying programme for my RTW trip though.
Also I get the impresstion that buying the PPT-AKL ticket separately will cost a fortune.