We just recently launched a podcast that has been top of category in iTunes for the past 6 weeks. We've done the same thing for two clients.

I would say that I would heavily use social media to get the word out about our stories. Also, ask your authors to help promote - the more people who know about the podcast - the more people will ultimately hear the winners. You could even possibly have a people's choice part of your competition - where people listen to the various podcasts and vote on the winner - that will get you more downloads.

We just wrote a blog post on our launch process which might give you some ideas - http://paychecktopassion.com/how-to-get-your-podcast-into-new-and-noteworthy/

And of course... what the previous two experts have already said.