Thanks Andy,

I've looked into the Oneworld RTW. But found that my selections for the US segments were very limited... there is no way to travel directly between cities on the west coast and once I got to LIH there is no way to get to SYD/AKL except via LAX, and that is not allowed.

Also the selection I get for aircraft types seems to indicate AA uses rather old ones....

A shame since Oneworld seems perfect for including that Cuba visit, but it then excludes any US destination.
This has led me to the conclusion that *A is better for visiting my primary destinations (US/NZ) than Oneworld. Allthough I like that there is no restriction on miles.