The point is, there are no physical leftover saves at all (no files in the directory and I never changed the directory).
There might be leftover saves somewhere, but you're not looking in the right place, or windows is showing the wrong place. FO has no memory of what saves are present after it is shut down. It's possible, but unlikely, that the GUI might show nonexistent saves if you had the game running and then deleted the saves, but this would probably only happen if you actually had the save file selection dialog open at the time. So, if you were seeing these saves in the GUI, there had to have been something on the disk to prompt their appearance in game. Whether logging out and back would remove these, I don't know.
None of [the saves] load.
This may be just because the save file formats are incompatible.
Any new savegames made do not register (i.e. are not saved to the disk).
This is possible; either the new saves are being put somewhere else than where it's finding the old saves, or the weird redirection windows is doing for some reason means the save fails silently...