I think part of why your analysis is so unconvincing to many here is that you are saying
You admitted above: “each individual measurement’s phase is scrambled” That means you can’t use it. Without phase information, the amplitude data is useless, end of story. There is a saying in meta-analysis: “garbage in, garbage out” and this measurement was attempting to spin garbage into gold.
However, you’re showing no proof of this. A common phenomenon in statistics that I, a non-scientist, know about is that data can on its own seem to be entirely random while in fact there is information present. You can combine that seemingly random data with other seemingly random data to get meaningful results. For a specific example, consider private key-public key cryptography. Data encrypted by a public key has no meaningful information that can be extracted just from that. But by combining it with the private key, which has no meaningful information, you can get accurate data: the original message. The hashed data is garbage and the private key is garbage, but the result is gold! So at least sometimes garbage data can be used.
It’s entirely possible that you’re 100% right here and the amplitude data truly is useless. But just saying “That means you can’t use it. … the amplitude data is useless, end of story” is not a proof. Because of this, if you want to convince the audience of non-scientists here, you will need to provide a stronger basis. Your current argument convinces no one that doesn’t already believe you or want to believe you. And inherently, someone who is coming here saying “I’m right about science and statistics and thousands of scientists and statisticians are wrong” is going to have to make a strong case for their evidence.