G. Mark’s Answer
You've stumbled on a situation very similar to my own. I went to school on a full scholarship that allowed me to take far more classes in more areas than would normally be well-advised ( :-) ) and had a tremendous amount of fun using up all those credits. And I've come up with the conclusion that very little of the knowledge you gain in so many areas is ever wasted. My first patent married computer architecture, brain research and music, and I sincerely believe that I would never have gotten it had I not studied things that seemed so unrelated.
Because of the value of general knowledge in innovation -- that of applying patterns and principles from seemingly unrelated fields to a problem -- it seems that the ability to see a problem from a new perspective works out well. In fact, some have estimated that over 70 percent of innovations come from using knowledge from areas different from the problem to be solved.
This is what I've found about managing a project. To get your hands around a problem that's difficult to define let alone solve, a "big picture" approach works. It works in ways that are unique to the human mind. Our brains do little else but find patterns where there don't seem to be any. History is full of examples, from the discovery of the benzene molecular structure to relativity.
So that's my suggestion. Take on a problem that's baffling others. Either run or join the project. Dig in. Contribute. Don't be shy about hypothesizing and sharing your weird ideas and your supposedly "irrelevant" observations. Your diverse set of skills will eventually "knock over that rubber tree plant" that others can't even see. Dive into unfamiliar waters. Probably not quite the answer you were looking for or expected, but humor me. Try it out. If nothing else, it'll be an adventure.