Lets take a page from Marx. Science is many things, in particular a relationship between capital and labor. The scientific method is a wonderful idea, but it is subordinate to the economic forces that underlie scientific activity. Look at the conflicts and contradictions between those doing science (labor) and those deciding the science to be done (capital), and that is the ultimate source of these crises.
The executive summary lists 40 points on how to improve the reproducibility of science. A bit over half of them are addressed to the sources of capital such as private organizations, universities, and governments. I think many of those points are good. However, I don't think the other points, the ones that recommend doing science in different ways, have a good punch. Even if you fix the problems there are today, so long as science is a rat race of trying to get grant money to stay afloat while burning out grad student after grad student, I think other pathological practices will creep in as a completely rational response on the parts of scientists to a hostile ecosystem. There's just a very big gap between how science should be done and what capital owners want from science.