It seems like one of the major recurring issues on this site (not that I'm speaking from any deep experience, since I've only been here a month myself) is that too many people are publishing stories with very little effort invested. Just look at the "New Storygame" page, and consider all the stuff that gets unpublished after a day or two because it's crap.
So rather than creating a contest to inspire people to contribute more crap, wouldn't it be more interesting to create a contest that motivates people to contribute something more noteworthy? Perhaps a summer-long contest with a September 1st deadline, inspiring writers to contribute something a bit more epic. Rather than 2 or 3 days, the participants would have 2 or 3 months to dazzle us with their talents.
Just my $0.02.