The walking in the desert with a compass in the hand is not an applicable analogy of the AE/FN situation.
They had two compasses, one magnetic one radio, a directional Gyroscope, and an autopilot. Also a drift indicator. To have set the autopilot to fly a course of 337 to 157 (with a wind correction of course) and maintain that course for 3 hours wouldn't be a monumental feat for a pilot, even one of limited skills as AE. The ten percent error in DR doesn't apply to an autopilot guided flight. They wouldn't have missed Gardner by 35 miles or even close to that.
Please remember that the prime function of an autopilot is to detect and correct for small deviations from a preset heading in order to maintain that heading. That is what "George" (the autopilot) did. Fred and Amelia monitored their progress (altitude, speed, fuel, engine performance, etc.)
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Harry, I don't know where you got the idea that having an autopilot to maintain the plane's heading eliminated all the factors that causes errors in dead reckoning. The autopilot maintains heading by reference to the directional gyro and the autopilot's directional gyro is no more accurate than the pilot's directional gyro, they both drift. And each of these gyros need to be reset by the pilot from time to time to agree with the pilot's compass so the same inaccuracies from this compass and the inaccuracies of resetting the directional gyros are the same for Earhart and for the autopilot. The only factor addressed by by having "George" handle the controls is possible inattention of the pilot in maintaining the heading, which is a small factor in the overall dead reckoning accuracy equation. All the other factors remain the same, such as wind shifts and gusts and inaccuracy in determining the actual wind by use of the drift meter (see:
https://sites.google.com/site/fredienoonan/topics/measureing-and-determining-wind-speed-and-direction-while-in-flight Noonan had a MK II drift meter, not the more sophisticated gyro stabilized models) and the subsequent error in determining the wind correction angle. Do you remember back to your student pilot days when you worked out a wind correction angle on your E-6B and determined the heading to hold. Did your computed heading ever work out to be exactly right or did you have to adjust your heading to aim at land marks in order to stay on course? Same problem when flying over the ocean but with no land marks available to make heading adjustments to stay on course. Dead reckoning on land or on the sea can be much more accurate than in flight because the factors that affect such dead reckoning are smaller and can be more perfectly known. Attached is an excerpt from
Navigation and Nautical Astronomy, the official navigation textbook at the U.S. Naval Academy, outlining these factors. In land navigation you do not have to stare at the compass but can pick out landmarks in the distance and aim for them which provides an accurate way to maintain your heading and you also do this when flying over land using "pilotage" but there are no such landmarks at sea so you are required to rely only on your compass and on your directional gyro that your set by reference to your compass, and George can't see any landmarks either.
Air Force Manual 51-40 states the 10% estimate of DR accuracy and the formula in U.S. Navy Manual 216 gives the accuracy for a plane traveling at 130 knots, such as Earhart's Electra, as 17%. These estimates come from the Air Force and the Navy, and guess what, Air Force and Navy planes have autopilots! I don't know how much time you have spent flying over the ocean but it is a lot different than flying over land with pilotage. See:
https://sites.google.com/site/fredienoonan/topics/accuracy-of-dead-reckoninggl