I don't think we even need a centrally manged list of game IDs now that we have game manager/installer apps. Just let each of those mange there own list of IDs. All the games need to do is reserve a bit of extra space at the start for the manager to store a game ID.
When the manager installs a game, it needs to save the old image including the ID, possibly with an option to disable that. It should then check to see if it has a saved eeprom for the game being installed, and if so install that. If not, it needs to get a new ID and set it in the eeprom. This may require running a small app before the main one, but it's certainly possible.
Working properly with multiple apps/platforms requires that they agree on a format for the saved eeprom image/ID pairs and cloud storage, but getting that seems easier than getting all game developers on board for an ID list.
It won't work for games in development, but that doesn't seem like a problem.