News!
I made everything again (EXACTLY as I did it before): Unistalled the game, erased all data and cache, reinstalled it with only my file in "Editor Data" folder.
Now the file works.
So, maybe the whole game's compatibility with the file's specific data gets corrupted when combining the file with some other custom data in a new save? That's my guess...
There must be a compatibility problem when the game tries to process the file in a new save.
And it doesn't seem to be a problem with competitions or structures, but rather with the data itself (Teams, players, etc).