Micromanage your community: send Survivors on errands, set them tasks, or send them on an adventure.
In Fallout Shelter you can build an 'Overseer's Office' in your base that allows you to micromanage your community and send individual Survivors on missions outside of the core map. Upon sending your survivor, a timer runs in the background until they arrive at their mission-specific location, but meanwhile you continue with the core game.
When the sent survivor arrives at their location, the game prompts you to take control of them. Upon doing so, a small map relevant to your mission is loaded alongside your survivor and then it's up to you to take control and ensure they complete their task. Upon completion, another timer starts until they return home with your reward(s).
I believe offering this feature through a buildable facility or the default radio centre would bring an exciting new dimension to State of Decay's core gameplay. It would give you a purpose to grow and train your community, it would allow bite-sized narrative content to be seamlessly integrated into your core game (and not a seperate entity) and it would give you another much-needed end-game goal to work towards. They could even vary in difficulty with harder missions being the equivalent of a 'dungeon' or 'raid'.
With regards to what these missions should be or how they should work, a great example is the original tutorial for Sod2. It's isolated on its own map, seamlessly integrated into the core game, and offers a more linear 'mission' with a focus on storytelling. This could even be a viable way to integrate Trumbull Valley into the core game.