If you want anyone to believe that the Island Radio Operators were a possible source of bogus Post-Loss Radio Signals, you will have to establish that they had the illegal crystal to transmit on Earhart's Aviation Transmitting Frequency's with their equipment.
Sorry, but you are operating under a misapprehension. Although it has been common for aircraft radios to be crystal controlled (and other types of radios designed to be operated by people without special knowledge and training such as CB radios), transmitters operated by trained individuals are more often tuned by use of a VFO, a "variable frequency oscillator," which allows tuning to just about any frequency you want, just like a common AM receiver. In order to get a ham license you must pass a test on radio design (this is one of the purposes of the Amateur Radio Service, to promote this type of education) so every one of the hams on those islands had the knowledge to modify and tune their transmitters to operate on 3105 kcs. This would have been especially easy (trivial, actually) since it was so near to the standard ham frequency band of 3500 to 4000 kcs, so would require only a very slight tweaking of the coil or capacitor in the VFO. It was very common then, (less common now that commercially manufactured ham radios are easily obtainable), for hams to design and build their own transmitters from scratch, many hams take pride in their ability to do this and in the quality of the signal put out by their "home brewed" transmitters. I have built several transmitters myself and none were crystal controlled. The same is true of the Itasca, they had professional technicians and also did not have a crystal controlled transmitter, as you stated in a prior post, so could adjust the tuning components of their transmitters to cover the frequencies requested by Earhart, 3105, 6210, and 7500. And just how did you think that they got their transmitters up on 31 meters (9000 kcs), it takes more than just inserting a crystal to make that large a change in frequency, it takes adjusting the taps on many of the coils and possibly modifying or replacing some capacitors in order to modify a radio to work on a frequency this far away from the previous operating frequency. This is a much larger modification than the trivial adjustment to operate on a frequency only 400 kcs removed from the prior standard ham frequency of 3500 kcs. It is obvious that if the hams could make the modification to operate on the 9,000 kcs band that they could make the much less significant change to tune to 3105 kcs.
The next time you are at your local library look for
the ARRL Handbook (Amateur Radio Relay League) which has been published since 1926, and you will see hundreds of plans for building various types of transmitters. Or
go here to see examples of home brewed transmitters made from scratch by hams using 1930's technology and some from plans published in the early editions of the
ARRL Handbook and in the ARRL magazine, entitled
QST. I have attached a photo of one such transmitter made from plans in the 1932
Handbook, it covers 3500 kcs (and other bands) and is tuned with a variable capacitor, not a crystal in sight. This transmitter could be retuned to work on 3105 kcs, possibly just by simply bending the coils so that the spacing of the turns is slightly different.
gl