On what distinguishes the two main branches of knowledge
You may want to take a look at the work of Lucio Russo as it is very relevant to the definition of science and its relations to the humanities. I would do no justice to his arguments by trying to summarize them here in a comment, so I might write a post on them later on.
The divisions you point to arise from the inherently divisive nature of that which all thinkers and their ideas are made of, the electro-chemical information medium we call thought. Thought operates by dividing a single unified reality in to conceptual parts. And thus, the overall human search for knowledge is divided in to categories and sub-specialities, which as you've suggested, then often come in to conflict with each other.
This insight seems useful to both science and the humanities, as both of these arenas are built of thought, and thus both are affected by the distorting bias for division which defines this medium.
Great post, thank you for sharing your thoughts!
Question: would not simulation be an example of experimentation, and thus be "more scientific"? By simulation I mean the mathematical/computational one whereby a person could study the effect on ecology of introducing a rodent on an island?