The fundamental problem is engaging them in the first place. Here's the real LPT: Don't play the game. Give the shortest possible answers and you don't have to play any games or remember any silly rules. You don't have to be rude, just short.
Me: I want to cancel.
Them: Oh! That's too bad! For our records, why are you canceling to day?
Me: Didn't want it.
[long pause as they realize that I'm not going to say anything more]
Them: Well, we have a great special today! Can I offer you 3 free months to stay?
Me: No thanks.
[long pause]
Them [now uncomfortable]: Was there a problem with our service?
Me: No, just don't want it.
Them [usually giving up by this time]: OK, let me go ahead and take care of that.
Works ALL the time. If you don't engage them, they have nowhere to go on their script. Usually I can break them within 30 seconds.