I led some students through a book study of Dr. Rupert Sheldrake's Science Set Free last year. I chose the book because it presents a quintessentially skeptical view of everything we consider 'known' and 'proven by science', and my goal was to get students to think broadly and critically (a skill that is sorely missing in academia today).
In the book, Sheldrake begins with an emphasis on the paranormal. He argues that, whereas the vast majority of people report having experienced paranormal activity at some point in their lives, 'paranormal activity' is terribly misnamed.
He also talks a bit about dark matter and dark energy, and the fact that the two combined account for (based on presumed models) over 90% of the 'known' matter and energy in the universe. Taken from that perspective, it seems that scientists (especially those probing the extreme cases of reality, and seeking deep fundamental truths, like yourself) should focus much more on how to explain or understand rare but widely-observed phenomena.
Also, take 'miracles' for example. Many of the things we assume to be 'impossible' within the context of modern physics, such as turning water into wine, are certainly theoretically possible, given the presumed existence of dark matter and how little we know about it. I am curious about how your simplified models might change if you added into the framework whatever dark-matter-to-observable-matter conversions would be required to explain the various 'miracles' that have been recorded throughout history. No doubt some (or many) of the various supernatural phenomena that have been observed across the ages are, in fact, illusory or otherwise 'false'. However, if even only a fraction are 'true' or have some level of truth associated with them, it might lead to some new discoveries in fields like yours.
Sheldrake also talks about the fact that 'perpetual motion machines' within the context of dark matter and dark energy are entirely possible, meaning that a machine could conceivably be constructed that converts dark energy or dark matter to observable energy. Such a machine would appear 'impossible' because it presumably violates the first law of thermodynamics -- even though it only does so if you narrowly define matter and energy as observable matter and observable energy.