Assuming you have made it to NZ via Oz-Lord Howe-Norfolk Island, take a deep breath and consider the following distances in nautical miles.
You mention Antartica; Christchurch to McMurdo is 2385, but, as has been mentioned, unless you have made private arrangements to have fuel shipped there you will be stranded.
McMurdo is not an international airport serving anyone who turns up.
Even if you have made your own fuel arrangements where are you going to from there ? the nearest airfield in Chile is probably about 4000mls away.
NZ to Chile island hopping.
Auckland to Fiji 1330.
From Fiji I havn't checked the various distances but I think,you will be able to island hop to Tahiti.
Tahiti to Easter Island 2644.
Easter Island to Santiago 2336
How is your 150kt cruise with an 8 hour endurance looking now ?