Here's a basic strategy for winning Snapdraft freerolls. You can also use a similar strategy to win the daily $5 freerolls offered at Draftbug. The Draftbug freerolls have the added advantage of paying cash to the top TWO finishers.
The key thing to remember is that only the these are large contests with top heavy payouts. There's no reward for coming in 3rd. That means that you shouldn't be seeking consistent performance - you should be using high variance, risky players who will increase your chances of an abnormally high score...even if there's also a chance of them being total busts for the day. Here's how you can do that:
1. Pick multiple hitters on the same team. Hitters on the same team (especially those near each other in the batting order) will tend to have high correlation in their performance. When one does well, the others will benefit. When there's a blowout, they'll all face the same 'garbage time' relievers. That means that if you use a few hitters from one team, there will tend to be more variance in your score. Some days you'll do really well and some days you'll do really badly. That's what you need to aim for in large field, top heavy tournaments.
2. Pick players who you expect others not to take. Once you play in a bunch of freerolls at Snapdraft or Draftbug you'll get a feel for which players are popular. Avoid those players. It doesn't do much for your chances of victory if Santana pitches a no hitter, if 15 other entrants had him on their team as well. However, on the (admittedly, less likely) chance that Scott Baker pitches a no hitter, you may very well be the only person who had him...giving you a huge advantage in the contest.
3. Pick control pitchers. This seems a little counterintuitive, but here's why you should alway take control pitchers. A high strikeout, high walk pitcher is going to have trouble finishing their games, no matter how well they pitch. Someone like Rich Harden just isn't that efficient. He's often going to pitch great...and still come out after 6 or 7 innings. In a contest with a less top-heavy payout, that may be great. But if you need to come in first, it's better to take a pitcher like Mark Buehrle. Although he really isn't as good, on the days when he gets lucky and does well, he has an excellent chance of pitching a complete game. In other words, his scores will have higher variance...which is what you're looking for in these contests.
4. Pick sluggers...even bad ones. Sluggers will tend to have higher variance in their scores. Anytime they hit a home run, they score well. Since you only care about 1st place, you don't mind that sometimes they'll strike out three times and have a negative score. High variance wins daily contest freerolls.
5. Don't worry about rain, benchings, and injuries. That's a slight exaggeration, but if there's a clearly superior option available, but you're worried that he might not get to play...stop worrying. You're going for first, and you need to increase your chances of a GREAT score, even if it also increases your chances of a really lousy one.
I hope this advice helps, or at least gets you thinking about strategy in large contests with only one or two spots winning. Also, if you haven't already done so, I'd definitely suggest trying out the Draftbug freerolls. While the site is similar to Snapdraft, it has some real advantages...including a public chat area that people actually use to swap strategy, ask questions, and talk trash.