First, if you are going to cheat, don't get caught. Or, at the very least, don't lose the game that you are cheating for. And remember, precedent has been set that it is a lost #1 draft pick, which, when you are going to fall in the Top 5-10 might be the final straw on the HC of the DB being sent to the unemployment line.
The Patriots had reportedly been warned at least twice before the Jets game that got them in big trouble, once in a game against the Packers at Lambeau Field and ... some other time before that. I can't remember and can't look it up right now. Not necessarily the same case here.
The moving of the Chargers or Cardinals franchises seem to make the most sense for two reasons: 1.) They are already out West, so the whole realignmet thing is still in place. 2.) They seem to have the poorest fan bases right now anyway.