After a couple more discussions, I'm happy enough to include a notoriety limit as an end game scenario. The implementation was relatively straightforward to include a notoriety limit and a check to see if any player has been over the limit in successive turns. Also decided to limit the submission of turns once there has been a winner as it's not that hard to reset the "completed" game if there is a consensus to play further. This also adds to the finality of the game as all that is left is to read the story produced.
Now that it's a game in its own right, the next step will be to break out the game creation into its own form, and then lock off the admin tab completely. There shouldn't be any need for people to get into the admin tab once the game gets going.