The same groups of people have been on those islands for a few thousand years though (not sure exactly how long but the language family spread is probably mid-Holocene which gives an upper bound). I wonder if there's any evidence for repeated bottlenecks (which you'd expect if the population had almost been wiped out a few times) ... people usually argue the opposite for that area but none of it's based on much evidence.
Would the links between the islands have been strong enough for the total loss of an island and its inhabitants to have been recorded in the oral histories of the remaining islands?
oh yes, I think so. There was heaps of connections between the islands and both mainlands.