I of course reinstalled the game (forgot to mention that), just didn't use those instructions (I also didn't use them the first time). SecuROM updated .exe files also don't fix it. I tried your shortcut trick, but it didn't help either.
I also just recorded a short video showcasing exactly what is happening, hope it helps:
Note that as soon as the problem occurs, my cursor appears (while during normal saving/loading it is hidden).