It sounds like an exciting project. I'm familiar with this class of tools and have just a few thoughts.
Some of your initial instincts are likely spot on. The number of "views" or comments, or for that matter votes, bookmarks, alerts, follows, etc. are all measures of "activity" which implies interest, which implies the value of the idea versus other ideas. The better idea management systems have an algorithm measuring activity as well as votes to determine idea "promotion".
Limiting the number of comments is also reasonable in this sense: Challenges should have finite periods of time; a beginning and an end.
Which brings up the notion of Challenges. A general idea box has the tendency to engender incremental innovation (doing things better). Most organizations are also hoping for breakthrough innovations (doing things differently) and that is almost always the result of a call to action of some sort ("Help us design the school of the future!").
There are tons of attributes that could make this better, but I understand you're working within a finite environment (there's a reason those systems cost so much money, they have 25 developers workings a dozen years adding features). But one of the most important is acknowledging contributions. You don't have to give away iPods or T-Shirts or cars to get people to contribute, but if you acknowledge their contribution they'll keep coming back. So a tote board of highest contributors, an email ("thank you for your idea", "someone commented on your idea", "Your idea has been promoted; selected") will keep folks coming back.