I think it's a pretty good idea to randomize the stories.
However, if you take the extra step to do so, maybe it's worthwhile considering a more radical change, and also reduce the amount of semi-finals.
Specifically, if you have 5 semi-finals, 3 with 8 stories each and 2 with 9 stories each, you'll be able to have 3 winners per semi-final for a 15-story final, which would both eliminate the earlier concern by MCWagner about the semi-finals being a bottleneck, and also reduce the amount of polls we all have to vote in.