Gary,
As far as their noticing that their Radio Direction Finder had problems at 1742 GMT when she said they were 200 miles out, she did not mention a RDF problem until:
1928 GMT: "KHAQQ calling Itasca we are circling [?] but cannot hear you go ahead on 7500 with a long count either now or on the schedule time on 1/2 hour"
(Was speculated by TIGHAR that "circling" was actually spoken as "Listening".)
1930 GMT: "KHAQQ calling Itasca we received your signals but unable to get a minimum. Please take bearing on us and answer 3105 with voice." Another radioman reports this message as: "Amelia on again at 0800 [local time] says hears us on 7.5 megs go ahead on 7500 again."
(For non RDF'ers; "minimum" is what she needed in order to get a direction {to the Itasca} as she turned that round circle loop antenna on top of the cabin.)
If they had done that an hour and three-quarters earlier ("200 miles out"), they might have even figured out the problem in time and at least established voice on lower frequency or even direction on lower still (Itasca should have also been sending 'A's on her 400 kHz Transmitter and that would have provided Amelia a Null or "minimum")...
Do you think she had tried earlier and just did not report her problem?
You don't think "WANTS BEARING ON 3105 KCS ON HOUR WILL WHISTLE IN MIC
ABOUT 200 MILES APPX WHISTLING NW"
at 0614 to 0615 Itasca time (1744 to 1745 Z) indicated that she was having a problem with her RDF? This transmission shows that she had not been able to get a bearing with her own RDF, I call this a problem. This was a complete change in the planned procedure, Earhart was supposed to take bearings on the Itasca, not the other way around.
And the same thing again just a half hour later at 0645~0646 Itasca time, 1815 to 1816 Z, see attached radio log.
Her message at 1912 GMT was "KHAQQ clng Itasca we must on you" do you think that might have been while they were following the LOP in from that DR'd 60 mile NW turning point?
Yes.
The final message at 2013 GMT was "We are on the line 157 337...We are running [on] line [north and south]."
If they had used an off-set, they should have been following the LOP only south and not north.
Using my example of a 60 NM offset when intercepting the LOP NNW of Howland, they would only fly SSE for 120 NM from the point of interception, twice the offset, at which point they would know that they had flown past Howland and that it was time to turn around and go back and look for the island.
This is from my website:"During this process you do not abandon your DR. By aiming off to one side
by the amount of the estimated maximum error in the DR at the point of
interception (60 NM in this example) you have converted a 120 NM
uncertainty along the LOP, 60 NM left and 60 NM right, into a 120 NM
uncertainty extending 120 NM left and zero right. This ensures that you
do not end up to the right of the destination. This allows for the maximum
possible error but, in fact, you are more likely to be nearer to your DR
position than to the extreme edges of the maximum possible error. When
you intercept your aiming point, 60 NM to the left, you are not surprised
that you don't see the island since it is most likely to be about 60 NM
to your right. As you fly along the LOP your DR also moves along the LOP
getting closer to where the island should be and you expect to see it
as you approach that point. Even if you don't see it when you arrive there
you are not yet worried because it can still be ahead of you. But as you
continue further and further along the LOP after the DR put you over
the island you start getting worried. But you must still proceed out the
whole 60 NM past where the island should be to be certain that you do
not miss the island. At the end of that leg you would know that you have
missed the island and would have to deal with that problem
most likely planning a standard expanding square search pattern centered
on the most likely point for the island."
As far as Fred taking over the Flight Controls of the Electra, I doubt that that would have happened unless Amelia came completely apart in the air. We don't know how much 'Stick-Time' he would have had in the Electra and more importantly, would have certainly taken away from his Primary Responsibility of Navigating... Such as it was.
You know as well as I do, since you are a flight instructor, that a reasonably smart chimpanzee can keep a plane right side up after it is established in cruise flight so Fred's lack of stick time in the Electra is immaterial. He might not want to try landing it but he would have no problem keeping it on heading and altitude. Once Earhart started to refuse to fly the headings that Noonan gave her, then his job as a navigator was over since the end result of his navigator's work is determining the headings to fly. What good would it do at that point to take additional sextant shots if Earhart is going to ignore the headings he computes from the sextant observations. At that point he moves into survival mode and does whatever it takes to save his own life.
gl