One night I did a bunch of research into what's involved in getting on the show, etc., and basically, here's out it goes (if you're interested):
1. Take a written test (for you, in Washington, I suppose), where they ask 25 (?) difficult ($800-$1000 level) questions in various categories. You need to get 20 right to hang around.
2. Later that day, if you got enough right, you go into a TV practice game, with a fake set and everything. They'll have you write down five interesting things about yourself, and after a practice Single Jeopardy, Alex or more likely some standin will ask you about one of those things you wrote down. You won't know which one he's going to choose, and you won't know exactly how he'll ask his question. You make a little pseudo-conversation with him, just like on the real show. Then you finish off the game, etc. What the producers are looking for here are people who can handle the TV aspect. From what I can tell, you sound like a perfect fit for them, but who knows.
3. I _think_ they tell you if you "pass" the TV test, and they say they may or may not call you in a month or two. From what I could tell, it was totally random whether or not they actually call you after that one-to-two month period - how well you performed on the tests had no bearing.
4. If you get that call in a month or two, you are DEFINITELY on the show (presuming you make the time and money committments) - you fly yourself out to California on whatever date they tell you, and pay for your own hotel, and then they'll film 5 shows per day. Sometimes it works out that you have to stay an extra day because of carryover champions. But as long as you get that phone call, they guarantee you'll be on the show.
All this comes from, again, being VERY bored one night and reading up on everything for four or five hours.
Good luck, and keep us updated Quik!