Bill, admittedly without knowing your subfield, it seems like you're in a good position to apply!
I think this is so hard because (1) it's probably one of the biggest professional jumps we've tried to take, and (2) the thought of not succeeding can be very painful (in a potentially deep, how-will-I-feed-myself, has-this-all-been-a-waste sort of way). From what I understand, successful applications require a touch of grandiosity--*this* is my 5- or 10-year plan, and I can *totally* do it, and it's the *most exciting* research you could bring to your department. (I realize that if anyone actually wrote or talked like that directly, they'd be snubbed, but that general sentiment seems critical.) And it's all very personal with no definite schedule. The last jump of this magnitude I probably took was getting into college, but the process was generally more distant and temporally constrained, and my odds were probably higher.
Because we all know that hiring is stochastic--that elusive "fit" you mentioned and variability in other candidates--it's probably a better strategy to start applying before we think we might be the ideal candidate. And with our minds' powers to reduce cognitive dissonance, we might just start convincing ourselves that we completely deserve what we're going after.
I just stumbled on this thread, which I find pretty reassuring and hilarious. It might help you too, Bill! http://chronicle.com/forums/index.php?topic=73013.0