Actually you don't even have to think up a story / setting for yourself; just take any old Agatha Christie novel and work out the time line up until the murder for each character.
Another problem you'd have to get around would be having everyone in the same room, as in: people being able to see the reactions of people who, in the story, are in other locations entirely.
Stopping and starting isn't a problem. All you need to do is leave long empty nothings at the end of each track in the playlist. When you want to go to the next step of the story everyone presses "next track" at the same time.
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