After some more searching I found the answer to my question here: Storyboards With Custom Container View Controllers
The solution involves embedding several container views 'around' the central UIView. Each of those containers changes the sets of controls loaded by swapping embedded UIViewControllers via custom segues. The logic for individual subview behavior is encapsulated inside embedded view controllers and the logic for swapping them is all inside the custom view container class. Very clean and extensible. The site above does a much better job of explaining it. Here's a link straight to the example on GitHub: https://github.com/mluton/EmbeddedSwapping
Some Apple docs that I also found to be helpful: