all beer styles have a different optimal temperature to be served at. and that is the temperature that the nature of that beer comes out the best. Serving a lager at 66 degrees is not going show off the best qualities of that beer, but serving ales at 60 degrees is not as bad. many ales styles are 50 degree beers.
Brew up a beer style that would be close to the serving temperature and enter that.
Look around for other competitions
and yes, it is not that uncommon for beers at competition to be judged at non optimal levels of chill