I had a crazy idea a while ago that the GM should be chosen by the leaders of the 2-3 largest parties so as to guarantee that the game's power brokers would have a shared interest in shutting down any backlash against unpopular story lines.
Seeing 2-3 makes me wonder if the way to do this would be to require a supermajority for removal and confirmation. I would also prefer that the GM be appointed independent of presidential terms- much like the Federal Reserve Chairman the post takes after. Not sure if there should be a fixed term, though I'm disinclined.