I once managed an essay contest with a \$1,000 award for the winner. The company I worked for carefully thought out the subject matter and rules of the competition, organized judges, then prepared advertising and marketing to draw attention to it. The investment of the company's time and money was considerable (the investment of my own time was more than I expected). How many entrants did we have? One (she obviously won the \$1,000).
Compare this to the U.S. town of Malad City, Idaho. When Idaho's lottery hits the half-billion range, the town is inundated with people buying lottery tickets. The town has rejected proposals to build more gas stations at the town's freeway exit to accomodate all the people who drive over the state line to buy the darn things. On any given day while the contest is running, there can be (I kid you not) 2X-3X the town's population standing in line to buy lottery tickets.
What's your point, JBH?
This contest is well intentioned and I very much applaud your effort and willingness to source the award. But the contest feels complicated. Volunteers need to post 20 unclosed questions (on this site...). Entrants must post 5 answers. You also need judges to donate their time. You haven't even posted the criteria for winning yet and already the investment of time is pretty high. In my experience, the more complex a competition is the more likely it will fail to meet your expectations.
Your contest should be simple, cheap, and have high value. The difference between my two examples is that one was complex to design and participate in without enough reward to entice people to invest in the proces — the other was dead simple: drive to Idaho and spend $1 on a ticket with the potential of winning hundreds of millions.
You're currently offering a complex process for a 100 rep reward. That's only half a daily limit that isn't hard to reach if you participate in the site regularly. (Heck, consider WillK, whose meteoric rise in rep comes from writing fun answers all the time. And kudos to Will! If he doesn't hit the magic 100,000 rep point today, he will tomorrow!)
I could easily be wrong, but this feels like you're creating a contest for the sake of creating a contest with the classic belief of "if I build it, they will come." I would very much like so see this effort succeed, and to that end I have a few suggestions.
Begin with a goal that doesn't actually have anything to do with the mechanics of the contest. In other words, have a better reason for doing this than the dubious fun of participating in a contest. In keeping with the Stack Exchange ideal, I would recommend avoiding large, vague goals like "to increase site participation" and stay as specific and focused as humanly possible. This is what made the Fortnightly Topic Challenges mentioned by a CVn popular: they had the very specific goal of building interest in just one tag.
You don't have a lot of options when it comes to advertising a contest. The ratio of meta users to main users has, I strongly suspect, dropped considerably as the site has matured (that would be an interesting graph...). You could post a Community Promotion Ad, but based on my own experience, it's a very hard sell to get people to even look at them — and you need a positive score of 6 just to invoke the ad. Which is all a very lengthy way of saying you need to worry about exposure, and the more complex your offering, the less likely your very limited exposure will react to it. Which leads me to....
Keep it simple. Simple, simple, simple, simple, simple. The bigger and more grand you try to make this, the more likely it will be ignored. A fair number of people on this site pop in at the end of a work day, have some fun for 30-60 minutes, then disappear for 24 hours. They have very little to invest no matter how fun they believe the contest to be.
Finally, I admire your willingness to do this, but the effort-to-reward ratio is very high, and it wants to be very low. The max rep for a bounty reward is 500. You might want to wait until you can offer that.