tobiashenry, unless I'm reading it wrong, it looks like you would qualify because your stopover would be at least 10 hours on a TK metal flight.
Now for a question of my own, for those that have done the stopover: is your luggage checked through to the destination, or do you pick it up in IST and check it again when you depart? If it's checked through to the destination, where do they keep it for 20 hours? The idea makes me a little nervous.