I agree that the a/c was intact enough on 8 July 37 to allow for transmissions but I also agree that some minor damage might have been done during the period 2-8 July. Betty's notebook offers indications of a struggle, possible injury(s), panic, etc. notably 'waters coming in. . .get out'. Do not recall the date of Betty's transcriptions, but wasn't it the 8/9th July? In any case, if you believe Betty's notes, something significant/serious was happening. Perhaps that was the start of the breakup, leading AE/FN to hastily evaculate to the beach. The absence of recovered removable/transportable gear from the a/c, either by the Oct 37 survery party, the native islanders over their period, the CG crew and TIGHAR searchers might suggest that AE/FN left the a/c in a hurry, not having used the preceeding 6 days to ferry possessions to the beach. Along with their other poor decisions, maybe they didn't realize they were in a "survival" situation until it was too late to do anything about it.
As for the natives seeing the wreckage and getting parts off it, I think whatever material they found and used for their own purposes was stuff that was swept along the reef, into the lagoon channel or onto the beach where it would be found and recovered at little/no risk. As Ric and other TIGHAR searchers can probably attest, doing anything on the edge of the reef is an extremely dicy proposition, and even the island natives, with all their skill and experience would likely shyed away from doing any extensive recovery operations there. Perhaps the 'ghost'story(s) related by Emily and others were nothing more than parents wanting to keep the kids from exploring a dangerous location and getting badly hurt.
Clearly something catastrophic happened to the Electra in that 38 hour window between the last transmission and the Navy flyover. Something serious enough to rip it off its landing gear, poke holes in the fuselage and wings and fill them with water. How deep is the water at reef's edge during high tide? Three or four feet? The latest photo of Nikumaroro from the ISS, in another thread here, shows what might be the start of a trench at the spot where the wreckage was supposed to be. Ric identified a hole at the spot where Nessie was supposed to be. Might that trench be nearby? How deep is it? What's the largest diameter of the a/c--8-12'? Add breaking 3-5' foot swells at/near high tide and its not hard to imagine the a/c being mostly hidden to someone not focusing their attention there anyway.