Thanks guys for all the replies (but what took you so long? )
The LAN option might work to Easter Island, but I understand the flights are packed from there to SCL, and I really wouldn't want to be stranded in either place.
I had my eyes on ANZ, too bad they don't want to play anymore.
And my company does not have an interline agreement with Air Tahiti Nui.
So with only a single option a day (AF), I will have to play it safe and spend the cash and a guaranteed coach seat.