They'll change your date if there's one available. The thing is, there aren't that many dates available before Dec. 1st. If you try after Dec. 1st, you might be able to get an earlier date b/c some people that got in to another school of their choice will cancel their remaining interviews. As of right now, though..i don't think you'll be able to get one.
Last year I was able to switch mine from a late January date to a Dec 4th or something like that only b/c I waited till after Dec. 1st to ask.
Good luck.