First, I have to agree with several other Monks who think your first suggestion is the best. Simply don't feed the trolls. Unfortunately, I have a tendency to do this. I keep thinking that a reasonable reply will convince them, but of course they're usually just trying to stir up controversy. So - I'll try to do better in the future and not feed the trolls.
Reaping would be OK, I guess, but once you start doing that, where do you draw the line? It's one thing to reap an empty post, or a duplicate. If you start reaping ones with content - even trollish content - it begins to resemble censorship. Who gets to decide what's a troll, versus just an unpopular, but valid, point?
Your idea of publishing Anonymous Monks' IP numbers seems to be excessive. Remember that there are valid reasons why someone posts anonymously, and many AM's post well-considered, respectful messages. Publishing their IP's would be punishing them for not being able to sign in (or being unwilling to do so). AM != troll.
So, yes, I'll try to restrain my enthusiasm when encountering trollish posts, especially anonymous ones. It's probably the best way to handle it. Being ignored is worse than being smacked down...