How did Amelia Earhart die?

Amelia Earhart survived the initial crash of her plane, made it to Gardner Island (Nikumaroro), then perished there

Question: How did Amelia Earhart die?
Position‹2 of 4›: Amelia Earhart made it to Gardner Island (Nikumaroro) and perished there or in surrounding waters.
Argument‹2 of 2: Amelia Earhart survived the initial crash of her plane, made it to Gardner Island (Nikumaroro), then perished there

The argument

There is additional evidence that supports the idea that the passengers of the Elektra did not die upon impact near Gardner Island, or very soon after landing. Instead, there may be evidence that Earhart and Noonan survived on the island for some time as castaways. A week after Earhart disappeared, Navy planes from the USS Colorado searched Gardner Island and found signs of recent habitation. A great many pieces of skeletons, artifacts, and signs of habitation have been found since Earhart’s disappearance, all pointing to the fact that shipwrecks or castaways had found their way to the island in the past. By 1938, the island was colonized as part of the Phoenix Islands Settlement Scheme, and colonists reported finding airplane parts, plausibly from Elektra. Furthermore, a colonial administrator discovered bones, two pairs of shoes (a man and woman’s), and a box that once held a sextant. TIGHAR estimates that the bones could come from a female roughly of Earhart’s build. Finally, at the Seven Site on the island, there is evidence of several campfires as well as the remains of birds, fish, turtles, and clams. Based on the way the clams were opened and the fish consumed, the products were obviously not eaten by a Pacific Islander.

Premises

[P1]Evidence suggests Earhart and Noonan may have survived as castaways on Gardner Island rather than dying on impact — a week after her disappearance, Navy planes reported signs of recent habitation, and later colonists found airplane parts plausibly from the Elektra. [P2] A colonial administrator discovered bones matching a woman of Earhart's build, along with a man's and a woman's shoes and a sextant box, and the Seven Site holds campfires and animal remains opened in a way inconsistent with Pacific Islander habits. [C] Taken together, this evidence indicates Amelia Earhart made it to Gardner Island (Nikumaroro) and perished there or in the surrounding waters.

Counter-arguments

Most detrimental to this theory is that the island was searched within a week of their disappearance. With access to fresh water, Earhart and Noonan should have survived well beyond this timeline and would have subsequently been found during the search. Beyond this, though there is much evidence that castaways have existed on Gardner Island at various points of time, there has been no conclusively found evidence (specifically DNA evidence) linking anything to Amelia Earhart.

Rejecting the premises

[Rejecting P1] Signs of recent habitation on an island in the Phoenix group establish only that people had been there, not who: Nikumaroro lay on Pacific sailing routes, had a documented history of wrecks, and was settled from 1938, so artifacts and even aircraft debris have several ordinary sources that do not require the Electra. [Rejecting P2] The Navy searched the island within a week of the disappearance and saw no one, which is hard to reconcile with castaways alive and signalling; the bones were assessed from recorded measurements rather than the remains themselves, which were lost, and no DNA or serial-numbered component has ever tied any find to Earhart or Noonan.