Story and gameplay isn't always mixing oil and water. This is a great example of how gameplay with a little planning is story. Simply by framing the things you do in the right way enables the player to be in that story instead of just hearing it. When you have the structure of how events will play out over time, you can still tell a pre-designed story with minimal effort. So instead of killing gameplay to leave room for story, just find the right gameplay to tell it and put your effort into structure.