Thanks for the reply, Ron, and for the countless hours of fun you gave me as a kid. :)

It looks fairly simple (famous last words), and the file size for save games is only limited by a user's available iCloud Drive space: https://developer.apple.com/documentation/gamekit/gksavedgame and https://developer.apple.com/library/content/documentation/NetworkingInternet/Conceptual/GameKit_Guide/SavedGames/SavedGames.html — looks like you just blob the save game data into a key-value pair with the GameKit API.