tl; dr - too long, didn't read.
I'm with Murray and, if I may be so bold, Triumvir. It is summed up thus: Win if you can, draw if you must, survive at all costs. Triumvir in particular has not yet been defeated, which is quite impressive.
So, if the stab leaves me in a better position of converting a survive into a draw, then yes I will do it, but if you find yourself in a situation where a draw is in the works that doesn't include you, then I would absolutely say that you should go Jannissary loudly to try to guarantee yourself a favorable result. In effect, you are trying to break up the draw group by offering one of them a better position and inducing them to take it.
The other time I've seen people throw a game is when one of the potential draw mates have so poisoned the well that one or more other players are simply not willing to help them. Spite can be a valuable motivator and played up if you can. Both strategies can be quite tough to pull off, though.
Of course, PPSC is an entirely different endgame in which long term alliances are easier to maintain since both players get something out of it.