Having more or less despaired of understanding R' Kook through his writings, which I generally find to be unreadable, I obtained "Essays on the Thought and Philosophy of Rabbi Kook" (edited by Ezra Gellman) from the local university library. It was a hard read as well, but at least it was straightforwardly written and the difficulty was in the conceptual analysis.
Based on my reading, I think the basic philosophical/mystical idea underlying R' Kook's thought is as follows:
(note - where there were gaps in what I learned from the sources, I added a little of my own thought as "glue" which could conceivably be in disagreement with R' Kook.)
The activity which best exemplifies God is creation. Similarly, the activity which best exemplifies the "image of God" in a person is creativity. Every moment of human creativity is valuable as an expression of the Divine image.
There are different examples of creativity in the world, some are a part of religious activity and others of secular or anti-religious activity. But since creation by definition stems from Godliness, even instances of apparently anti-religious creativity have some religious value.
Creativity does not take place in isolation: your creativity builds on developments picked up from other people, even people you disagree with. In war and commerce there are winners and losers, but in the world's intellectual development there are no losers, since one person's ideas supplement rather than replace the other's ideas. Thus the world is always progressing, never regressing or standing in place.
More creativity effectively means more revelation of God. Thus, all the instances of creativity in the world add up to a dialectical kind of evolution, with the final destination being the ultimate (complete?) revelation of God in the world.
So that is what I discovered. It seems to me to be an innovative, yet logical, development from previous kabbalistic thought. Sort of a generalizion of kabbalah from a set of technical concepts to encompass a broad range of human experience. Extremely brilliant, in my uneducated opinion.
I remain, though, with one question which I had before picking up Gellman's book and which the book did nothing to answer. Essentially:
The above approach assigns value to every intellectual possibility. But it is insufficient to decide which possibility is more valuable than the others, in order to decide on a course of action. Indeed, such a decision may be fundamentally problematic for R' Kook because it requires fragmentation in one's view of the universe (examining each action independently without regard for the other) rather than maintaining a unified overall perspective.
If so, then what if any application does R' Kook's thought have to the world? What is the unavoidable practical difference, the "nafka mina", between his approach and that of any other authority? And if there is none, what value does the philosophy have except as an intellectual toy?
I do not have an answer to this question. The approach of some of his followers that "conquering land is the only mitzvah nowadays" does not seem to me an authentic representation of R' Kook's views - much less a morally viable approach to life.
My best idea for finding an answer is to examine R' Kook's letters and other practical documents he wrote during his life, looking for examples of where he differs from other rabbis, and more importantly, examples of where his philosophy directly influenced the conclusions.
But that kind of analysis would take a huge amount of work, so don't anticipate seeing it anytime soon on this blog.