Excellent work tracking down the repeatability. Sadly, this implies it's an issue we struggled with for over a month, before literally rolling back the entire project to a version of Unity from 2015. It's probably a problem in Unity itself, we were unable to get any form of useful error message, and the crash happens at random parts of the saving process (implying there's a second thread, made by Unity, which either times out or crashes).
The best we're likely to do is to try to compress the save files down a bit before they're passed to the save/load function, and decompress them at the other side. There are some easy ways to do this, and some hard, so we'll see how many we can get done for the next version.
Regarding the private data in the output file, that's just yet more annoying Unity stuff. In general, I think Unity's a decent enough engine, and the game wouldn't be possible without using a third-party engine like this, but some of the decisions the devs made are perplexing to me. My name is in the credits and the github repo, so I'm not too concerned, it's just irritating and odd.
Thanks for your work tracking down the issue, sorry that I can't promise a full fix. We'll look into what can be improved.