Nice. Some really cool ideas to unpack in there. First though, while it is true that the idea of coincidence does bother many scientifically minded folks, it is not the case that little or no scientific research has been done on the topic. In fact there is a fairly vast literature of studies in statistics, mathematics, psychology, neuroscience and probably other fields as well where the “problem” of coincidence has been studied in one way or another. Many books have been written on the topic. The mathematicians/statisticians typically like to try and calculate the odds of certain coincidences occurring or develop models to predict them. Especially in probability theory as it relates to the law of large numbers. https://www.scientificamerican.com/article/math-explains-likely-long-shots-miracles-and-winning-the-lottery/

and

The psychologists and neuroscientists of course try understand the mental cognates of coincidence. What happens in the brain when we experience a coincidence? Why do we consider some events coincidental but similar events that have identical probabilities of happening as not? Why do we feel so “strange” when we recognize that something is a coincidence? and the list goes on and on.

More to say later….