That it takes a while to figure out struck me on reflection as a good thing. You want a character to be complex, to have if possible all of the inner confusions and contradictions of a real person. If you set out to write someone thinking, "this person is ambition" or whatever, you're going to wind up with cardboard, because real people don't act the same way all the time. Ask anyone to describe themselves in one word and they're likely to fidget a lot, come up with something, and then add "but" to whatever they said.
I think that this notion of a core characteristic is something that should emerge as you get to know the characters, and it's not likely to make itself known in the first draft. Once it comes out, you can shine it up in a few places if you want to, or leave it as an exercise to your future readers to argue about; if you can't come up with anything at all, though, after several drafts, that might mean that your character is not drawn clearly, or isn't being active enough to demonstrate their qualities.