Actually, I am not super certain what EditAnywhere or VisibleAnywhere do. They seem like they do the same for some reason. But that is probably just my lack of understanding. I should probably read up on it a bit more and maybe look at the source code or something.
That being said, I think you were right that it was a corruption issue or something like that. As part of a troubleshooting step I realised that if I rebuilt some of the blueprints from scratch with a new blueprint class, the issue would go away. So I sort of did that for all the scripts to avoid the issue. After that, everything started working perfectly again. So there was definitely something weird going on that was not intentional behaviour.
Thanks for the help.