Structure of title
Solution 1:
I think you're making a conceptual mistake here. The structure "Part 1 of Title: Part 2 of Title" does not tell which part is more important than the other. Consider some titles
Genius: The Life and Science of Richard Feynman,
Uncertainty: The Life and Science of Werner Heisenberg.
Clearly, the second part of the above titles are the most important, as they tell you what the book is about.
Albert Einstein: A Biography,
Edward Teller: The Real Dr. Strangelove.
And clearly, the first part of these titles is the most important.
If you are going to drop one part of the title, and just refer to the shorter part, the convention is to drop the second part. So for that purpose (and probably only that purpose), the first part is the main part. But note that you can't always do that unambiguously:
Pirates of the Caribbean: Dead Man's Chest,
Pirates of the Caribbean: At World's End,
Pirates of the Caribbean: On Stranger Tides.
For this last movie, you would have to refer to it either as "On Stranger Tides" or "Pirates of the Caribbean 4".
Solution 2:
For reference purposes and shortened citations, use the first part of the title. 'The Quest for Freedom' is the title, and what follows the colon is the subtitle.