I offer another purely hypothetical scenario, and I stress hypothetical because as we all know I have a quite serious reluctance to accept the validity of much of the cited physical evidence, however in fairness it is one that bears consideration.
The Electra ran out of fuel and came down at sea and sank. Either Earhart and Noonan or both of them made it into the life raft which eventually drifted ashore at Nikumaroro. The survivor lasted long enough to die on the island which explains the skeleton, and also the lack of any wreckage so far found - it might explain possible personal items like the freckle cream and the compact. Those being in a bag hastily grabbed as the plane sank.
However I stress that that is highly conjectural because the skeleton is missing and the later reinterpretation of it from Hoodless' notes cannot be confirmed, and the items like the freckle cream, shoe parts etc. cannot at present be shown with any confidence to have belonged to Earhart alone, as distinct from any other visitor or inhabitant of the island. It does however explain the lack of aircraft wreckage (the native reports are of dubious value, to say the least), and the very weak state of a survivor who is unable to attract the attention of the Navy searchers. It leaves out the post-loss radio messages, none of which are highly convincing - simply because of the admitted frauds and hoaxes, one out all out until proved otherwise.
That would put the wreck in very deep water, possibly to the north west of the island because of prevailing winds which would push the raft towards the island. Highly conjectural and not my favourite scenario.