Okay. It is fixed.
The issue was the third-party open source library we were using to save/load was based entirely on a recursive algorithm. Once the number of people grew too large, it kept just going through their social relationships, calling the recursive function each time it encountered a new person. As such, the thing hit a stack overflow due to having, for every person, called a new recurrence of the function.
Technically it worked, it just scaled so badly that once people hit a certain threshold Unity died.
I've reworked how people refer to one another. The new implementation is technically ugly, and goes against accepted best practices, but it at least works.
At least, I hope. New bugfix version is available for download.