I don't agree with your proposed way of studying this. You're trying to study a symptom and then conclude on the cause of the symptom. That makes no sense. If you want to prove that Facebook is listening, then prove that Facebook is listening. And don't try to prove that Facebook is listening and then targeting you with ads based on what you said. There are way too many levels of indirections that can trigger false positive for a vast number of reasons you don't control at all.
What you are trying to do is replicate in large-scale displays of anecdotes but with a slightly more controlled environment.
That won't prove anything since it will just be anecdotes and will again not sustain rational explanation by experts of Facebook ads mechanisms.
Without getting into the ads delivery part and the anecdotes, how would you prove that Facebook is listening?
How would you prove that there is a set of information taken from your speech or your audible environment transferred to Facebook.