What's the probability the LHC will save the world? That either some side effect of running it, or some knowledge gained from it, will prevent a future catastrophe? At least of the same order of fuzzy small non-zeroness as the doomsday scenario.

I think that's the larger fault here. You don't just have to show that X has some chance of being bad in order to justify being against it, you also have to show it it's predictably worse than not-X. If you can't, then the uncertain badness is better read as noise at the straining limit of your ability to predict - and that to me adds back up to normality.