I am on Stack Exchange's new CHAOS team and while posting a question like the narwhal question, that's ripe for meme-style attention, is certainly a "chaotic" thing to do, that sort of activity is not the goal of our team. My coworkers and I did not intend to bring negative or unproductive attention to Skeptics.SE. I simply got a little too tongue-in-cheek with the phrasing of my question.
All of what I posted in the question is true. We do have a coworker who believes narwhals are a myth, like unicorns and jackalopes. We did try the methods I listed in the post, and she continued to think we were pulling her chain.
So I posted on Skeptics.SE believing it was a place to get a legitimate answer - not to "are narwhals real?" but to "how do I convince a skeptic that something exists without either of us leaving the room?"
I feel the latter could be an appropriate question. I read the FAQ before posting the original question and felt like the core of our question was on-topic. I think that where I went wrong was in choosing a flippant, joke-y title and theme for the question. With the community's permission, I would like to post a new question in a more professional manner and see what answers Skeptics.SE can come up with.