HUGE logic flaw:
If the British expedition that was tasked with evaluating if the island was uninhabited, then they would have noted the wreckage of an airplane in the shallow water. The Brits are notorious for detailed observations and especially for writing everything down into log books.
It’s not reasonable to assume that the 1937 expedition of Gardner Island would be both oblivious to the Earhart news and also not note if an airplane wheel what sticking out of the surf right in front of their bow.