You're right about one thing, Patrick—we can't win. Tournament pools are the bastion of the idiot savants of the world, which means we're out of luck (though by the end of this week we'll all look like idiots, I'm sure). On the other hand, I did surprisingly well with my Oscar picks for the same reason.
I agree that chalk is the smartest way to go. Picking Iona to reach the Sweet 16 doesn't make you an inspired, outside-the-box thinker—it makes you a moron, and almost certainly a loser in your pool.
Since I routinely lose to people with little to no sports knowledge every year, I can only offer a best guess for beating the bracket: Pick chalk, along with one or two sleeper picks. Unless we get a repeat of the mechanical 2007 Big Dance (Elite Eight of four one seeds, three two seeds and a three seed) there will be at least one bracket where a mid-level seed makes a run and even reaches the Final Four.
Generally, look for teams with tournament experience who are seeded between, say, three and seven (Michigan State's recent Final Four runs are the best example of this). Beyond that, here are a few bona fide sleepers:
Louisville: A no. 4 seed in the West, the Cardinals will be dangerous if they can get by New Mexico in a virtual away game in the Round of 32 in Portland. The Cardinals win ugly (they beat Cincy 50-44 in the Big East championship game) and they can frustrate no. 1 seed Michigan State and no. 2 seed Missouri by slowing the game down. Also, Peyton Siva is a legit star in the making.
Gonzaga: A tired sleeper pick, I know. But as the no. 7 seed in the East, they likely draw an Ohio State team in the Round of 32 that is prone to coming up small in March Madness. And the Zags can shoot as well as ever. They could easily end up in the Sweet 16.
Florida State: After watching them beat Duke and UNC on consecutive days this weekend, I'm a believer. As a no. 3 seed in the East, they would benefit from a Gonzaga upset of Ohio State and appear too athletic to be bothered by no. 1 seed Syracuse's zone defense. It would not be at all surprising to see the Seminoles in the Final Four.
NC State: This is a Rip Van Winkle-level sleeper pick, as the Wolfpack are a no. 11 seed in the Midwest. But VCU showed last year that an 11 seed can make the Final Four (as George Mason did in '06) and NC State will be playing with a chip on its shoulder after a 69-67 loss to UNC in the ACC tourney semifinals, which many thought was marred by questionable late-game officiating. An NC State-Georgetown Round of 32 matchup would be scintillating, an NC State-Kansas Sweet 16 game even more so.
Do you believe in the power of sleepers, Hampton? Or is chalk (as in Rock Chalk Jayhawk) more appealing to you?