Break up your storyboard into multiple storyboards.
There is no reason for your app to contain only one storyboard. Break your storyboard up into module storyboards. You can use +storyboardWithName:bundle: to load storyboard modules.
See: UIStoryboard Best Practices for other good storyboard ideas.
Update
It’s important to note this is not a complete solution to the problem. In the same way you cannot completely avoid the possibility of merge conflicts in source code decomposing a giant class into smaller modules, you can’t avoid the possibility storyboard merge conflicts either. The idea is to reduce the likelihood until it becomes a manageable problem.
There will alway be tricky merge situations in a large codebase. A properly decomposed solution will reduce the number of conflicts and minimize the number of lock out needed.