You are right, it is problem, but I suggested a possible patch in Update 2: The idea is to create copies not of S(t) moment, but only of the next moment S’(t+1), where the pain disappears and S is happy that he escaped form eternal hell.
In your example, it will be like to procreate healthy children, but tell them that their life was very bad in the past, but now they are cured and even their bad memories are almost cured (it may seem morally wrong to lie to children, but it could be framed as watching a scary movie or discussing past dreams. Moreover, it actually works: I often had dreams about bad things happened to me, and it was a relief to wake up; thus, if a bad thing will happen to me, I may hope that it is just a dream. Unfortunately, it not always works.)
In other words, we create indexical uncertainty not about my current position but about my next moment of experience.