Even if she did defy the odds and hear AE one time
I have to say this is fascinating. Some thoughts:
The official odds that Mrs. Paxton heard Earhart on anything lower than 24840 kHz, as cited in the radio message catalogue, are one in one quadrillion. With all due respect (and respect is due, IMHO), it's really hard for me to see that as just defying the odds. That's more like defying the laws of space, time, gravity, and whatever else remains of physics all at the same time. (I take the number literally, as a mathematically derived probability, as I think I was intended to.)
One quadrillion is a number so huge as to beggar human comprehension. It's the number of stars in about 10% of the entire universe that we can see with the best telescopes. For all practical purposes, the odds were zero.
Yet Nina Paxton wrote to Time Magazine on July 14, 1937 that she was listening on the "band between 12 and 13 mHz" (2nd harmonic of AE's day frequency was 12.42 mHz) and heard Earhart with a reception that was "anything but weak."
Ms. Paxton's official status concerning her report is "not credible." Maybe she heard something that just wasn't there (and got lucky in naming the right harmonic). Maybe she was a hoaxer. We can agree she embellished, invented, over-interpreted, misremembered, and altered her story over time. But Matt, if she "did defy the odds and hear AE one time" her status, in my opinion, is probably closer to "uncertain." And if, however she reported it afterward, if whom she heard was AE that one time, it means that the radio propagation to frequency probabilities might warrant a second look. But those are the possibilities, as I see them. I'm absolutely willing to entertain more if I'm missing some.
Other than that, I agree with everything you've said. (I think identifying the Philco in the photograph was most impressive, btw.)
Joe Cerniglia
TIGHAR #3078R