Even if there was a short story contest for such an ENT collection, the small print would undoubtedly mean I couldn't enter. Typically not open to non U.S. residents and all that legal business.
But, I can see that idea being a success (at least in terms of entries, obviously don't know about quality). What with all the fan ideas and road maps that have criss-crossed the web since the cancellation. Pining after those lost years, seems to be the main lot in life for fanatics of the show... Oh yes, you bet your life we're out there!