Garjel has a point. Since there could be so many people writing large entries (given that this will be a monthly thing, these entries could get up to novel size if people get really serious), it could get just too hard to read everything.
Not as if I own the place or anything, but I'd like to make a little suggestion: What if we classified the pieces by length? Maybe have different word number classes, each with their own individual vote. After voting was done, perhaps the winners (top two, top three, whatever) from each length class could be put up for the finals and the winner decided out of them.
It's more complicated, sure, but solves the problem of simply not having enough time. If you want to have input, but can't read the longer ones, then you can just vote for the shorter ones. The finals would bring out the best in all length classes, I can definitely see smaller stories winning the finals due to their creativity and charm, even when put up against the pieces in the larger classes. Certainly not a perfect system, people could end up being just too lazy, but perhaps certain people in the staff could vote in the higher classes in order to get actual opinions in there.
Again, not trying to run things or anything like that, just sharing an idea. With any luck, more ideas will come in and you'll be able to pick a good one or throw them all into a blender and get a superior franken-idea.