Just guesswork - not even a theory - but I wonder if they could be some kind of acoustic phenomenon, like the patterns that will appear in sand on a flat surface when a violin bow is played across its edge, or water patterns in a Tibetan bowl? I'm not sure they really look like that, but maybe it should be considered.
One oddity that I don't think has been mentioned yet: are there any reports of poorly formed circles, as you'd expect when people are learning to make them with planks and so on? You'd expect some practice ones from people new to doing it.
The Chladini patterns are far more symmetrical and don't have the huge amount of variables found in crop patterns .
There probably are plenty of farmers who have woken up to a mess in their cereal field but it's not going to make the news .