A lot of work might need to go into this answer, but I can certainly vouch for the Australia - NZ part of it. West to East is certainly the best option. The jet above FL310 is usually in excess of 120-150kts, obviously differing with seasonal variation.
Can't recall ever seeing a decent tailwind the other way, the physcis doesn't really support it...
Dunno if this helps or not, it's only a small leg considering.
