The GameID has nothing to do with the cheats. The gameID is nothing more than a HASH check. If you check the gameID on the patches that WORK with cheats you'll see that the gameID is different too.
Before, I replaced files of the same size, so all the data stayed in the same place. This caused some errors because I had to pad some files to make them the original size.
In 3.1, the files aren't padded, and are smaller than the oirginal. This causes all the data to shift.
AR codes work like hex editors. They say: Point to this location in the data, and change it to this.
However, if the data is shifted, the AR codes will be pointing to the wrong data.
I'll work on fixing the Giratina Origin form when I get to that point in the game.
I currently have 6 badges.