So I'm assuming the missing world appear when you run the game in vanilla.
Could you try to open a save file in vanilla that was created with forge mods that you don't mind possibly losing (or just make a test one in forge) and tell me what happens? I just want to rule out the possibility of the saves actually being corrupt.
Are the regular files in the saves folder or are they empty?
Also, do you have any mods that are modifying the main screen, terrain generation, coremods installed that may cause issues?