First of all let me say that this is an excellent and well
researched question. A quick recap from Wikipedia is handy:
Outside the mainland of Afro-Eurasia, [...] megafaunal
extinctions followed a distinctive landmass-by-landmass pattern
that closely parallels the spread of humans into previously
uninhabited regions of the world, and which shows no correlation
with climatic history [...]. Australia was struck first around
45,000 years ago, followed by Tasmania about 41,000 years ago
(after formation of a land bridge to Australia about 43,000
years ago), Japan apparently about 30,000 years ago, North
America 13,000 years ago, South America about 500 years later,
Cyprus 10,000 years ago, the Antilles 6000 years ago, New
Caledonia and nearby islands 3000 years ago, Madagascar 2000
years ago, New Zealand 700 years ago, the Mascarenes 400 years
ago, and the Commander Islands 250 years ago. Nearly all of the
world's isolated islands could furnish similar examples of
extinctions occurring shortly after the arrival o