HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

Well, there's an extreme option. Just replay the turn transition without HD, on the classic SOD, then save and continue the game. Although it won't work with passwords...

You can remove the password, though. Load the starting map and remove the password. But this should be done by a third party. I'm just afraid that the save file still won't be recognized.
HD mod used to fix SOD bugs, now it's time to fix the mod's bugs with the original game. :)