I've really enjoyed writing the beginnings of novels and really enjoyed writing the endings of novels. The middles have always been the unpleasant slogging parts.
Frankly, I wouldn't do too much regarding this contest until I'd won it. Write the best scene you can, write a good synopsis. Don't start it early -- all that'll happen is that you'll most likely NOT win the contest, and then you'll have a really big fanfic piece on your hard drive.
If you have the time and energy to write a novel, write your own. Don't worry about this contest unless your ten-page synopsis comes back.
Incidently, 10 pages in manuscript font is about 2500 words -- a not-long short story. Courier 12, 1" margins, double-spaced. That's manuscript format.
-Tacky