Scenario: Plane lands on reef edge, landing is rough enough to injure but not incapacitate occupants. After recovering some strength the crew disembarks and pilot injures ankle negotiating reef flat. Walking in the surf is very difficult so life line is tied off from plane to trees along the shore. Radio calls begin and continue for several days. Crew explores vacinity of shore around airplane, find boats and debris from Norwich City. Tides continue to rise until plane is torn off the landing gear and is submerged in the surf. Crew forced to shore. Search Planes fly over. Crew unable to draw attension for whatever reason, asleep? exploring in bush? unable to walk quickly enough? In time castaways move to "Seven Site" where one or both perish under the ren tree....
I have attached two photos from the Purdue collection. The first photo show what the Electra must have looked like standing on its legs so that the engines were high enough to be run to provide the electrical power so that Earhart could send out radio messages. The second picture is of the plane after it crashed on takeoff from Hawaii.
You believe that Noonan was injured during the landing on the reef at Gardner island, a landing that would have ended up with the plane in the position shown in the first photo. However, when the aircraft ended up looking like it does in the second photo, Earhart, Manning and Noonan all walked away without injury. This crash was sufficient to rip off both main landing gears and did substantial other damage to the airframe. I don't know, but it seems to me that if Noonan was not injured in the crash at Luke field then it is very unlikely that he was injured in the controlled landing on the reef. And, keep in mind, nobody had any warning of the impending crash in Hawaii so as to brace themselves to avoid injury but there was plenty of time to prepare for the landing on the reef, it did not come as a surprise, making it even more unlikely that Noonan sustained any injuries there.
Your only reason to believe that Noonan was injured is the message that Betty claimed to have heard. See
Brandenberg's original analysis of the probability of Betty hearing Earhart. This shows only a one chance in 878 and that only existed for the first half hour. In the next hour the probability of Betty actually hearing Earhart dropped off to only 1 chance in 344,827! For the last 15 minute period the probability increased to 1 chance in 50,000. The current listing for the Betty reception doesn't break it down into these three periods but it makes sense that the periods mentioned in the first Brandenberg table also hold true for the current listing, so after the first half hour the chance of Betty continuing to hear Earhart dropped off to
Brandenberg's new estimate contained in the new listing of one chance in one-million-four-hundred-ninty-two- thousand-five-hundred and thirty seven (1/0.00000067 = 1,492,537) yet the claim is that Betty heard Earhart for an hour and 45 minutes. Or to put it another way, even Brandenberg, using all of his electronics acumen, ends up showing that the odds
against Betty being able to hear Earhart for the period that she claimed is 1,492,536 to 1. Wait a second, isn't Betty the same person who claimed to have won the Mega Millions Lottery last week? Wait, no, that was somebody else. So do you really believe that Betty actually heard that Noonan was injured?
gl