Sounds interesting. Perhaps actually having the game there, but also being able to bring up a game menu, and in it have the option "Skip to next Plot Point." then the player can stop playing that section, and they will immediately move on to the next section, with the story continuing. Then give the player 2 options when the story telling is done, "Back to game mode" or "Skip to the next Plot Point".
play it through and you can go back and change things.