Having only had this happen to me once, I can't comment with any depth on solutions. I can, however, tell you that in that one instance, our spontaneous group solution of paranoia and delusion definitely salvaged the fun for a few of us.
The basic plot of the game was that we were all mid-level nobles in a kingdom that being politically destroyed by another and we uncovered the plot by literally stumbling onto a body. That was the first and only death for two gaming sessions. The rest was political intrigue.
But in the third session, one of the NPCs made an off-handed remark about a noble woman who was involved in the plot, calling her a witch. He meant it as a generic insult, but one of the other players latched onto it and started looking for evidence that she really was a witch. Some of the other players caught on, and soon our characters were convinced that they weren't just saving the kingdom from political upheaval, but from the Vast Eternal Forces of Darkness.
The GM got frustrated when, instead of weedling information out of NPCs about the political crap, we started torturing them and trying to get them to reveal their blackened corrupt souls so we could dispatch them in the name of goodness. But after a while, he stopped trying to debate us into behaving the way he thought we should and just accepted that our characters were convinced Evil was afoot. The fact that we weren't actively trying to ruin his story line helped. In fact, we continued chasing the conspiracy he had developed, we just changed our characters motivations for doing so and were a lot more over-the-top in our actions. The game plot moved on in spite, or because, of the handful of us who went off the rails, and even the players who weren't "acting up" still had fun trying to keep us in line.