You seem to be equating saving someone from death with them living literally forever, which ultimately appears to be forbidden, given the known laws of physics. The person who’s life you saved has some finite value (under these sorts of ethical theories at least), presumably calculated by the added enjoyment they get to experience over the rest of their life. That life will be finite, because thermodynamics + the gradual expansion of the universe kills everything, given enough time. Therefore, I think there will always be some theoretical amount of suffering which will outweigh the value of a given finite being.

Your writing feels comically-disturbingly wrong to me, I think the most likely cause is that your model of "suffering" is very different from mine. It's possible that you "went off to infinity" in some direction that I can't follow, and over there the landscape really does look like that, but from where I am it just looks like you have very little experience with serious suffering and ignore a whole lot of what looks to me to be essential complexity.

When you say that all types of suffering can be eliminated / reversed, this feels wrong because people change in response to trauma and other extreme suffering, it (and the resulting growth) tends to become a core part of their personality. There is no easy way back from there, in a way this is also non-reversible. Removing a core part of their personality would effectively destroy them, replacing them with a past version of themselves feels equivalent to killing them, except it also devalues their struggle and their very existence.

Getting the decision on whether (and how far) to reset from anything other than their current self takes away their agency. The different versions along time are (potentially very) different persons, singling out any one of them and valuing it higher than the others is bound to be problematic. I doubt that you could find a consistent valuation within the strands of the person over time, and imposing some external choice just creates a hell (tho it may not be apparent from inside.) I don't think that this is something that you can "magic away" by sufficiently advanced AI / singularity. (And if you think that arbitrary editing of the person has already taken away their agency…? Well then you still have the same problem of identifying the point where they cease to be mostly self-determined, where they cease to be "them", and the "torture meta-game" will have shifted to make that maximally hard.)

So the best that you could achieve is probably something like having multiple independent versions of a person exist in parallel, but at that point you're not erasing/undoing the suffering anymore, and some versions may well want to cease to exist – for them, this will have been a fate worse than death. (At this point the "best" strategy for the 100 billion year torture meta-game is probably to allow just enough space for recovery and growth that there's a high chance that the person wants to continue existing, not sure that's better…)

By this time we're dealing with multiple versions of possibly arbitrarily rewritten copies of a person… and at this point, we're basically in situations that other commenters described. It would be no harder to resurrect from traces of physical remains… (If you can recover the original process after billions of years of deliberate, directed reshaping, then surely recovering it after a mere thousands of years subject to mostly random bio/physical processes should be trivial in comparison, right?) …or outright create new persons from scratch… (Who could tell the difference, hm? And if anyone could, would they feel safe enough to point it out?) …than to deal with all this "undoing of suffering". Now look again at your question:

If you press the button, you save 1 life. But 7 billion humans will suffer from the worst possible torture for 100 billion years. […]

I don't think the answer is yes.

Interesting concept, I have a few questions:

Does this apply only to humans, or are there also some non-human beings such that any amount of human suffering is preferable to accepting one of their deaths? Is there a clear cut-off, or is it possible that there could be beings for which some amount of human suffering would be worth more than the death of such a being?

Are there humans sufficiently brain damaged such that while their bodies are still alive, their minds are sufficiently poorly recoverable (even in theory) that the moral imperative isn't as clear?

Is it ethically mandatory that we invent caretakers that can imprison all humans in padded rooms (or vats) for their whole lives whether they want this or not, to ensure that they can never trip over and bash their brains out?

How does this theory handles cases where death is inevitable, such as (say) universes in which total computation is finite?

Is a far enough divergence from a previous mental state, such that the previous one can't even be approximated any more, equivalent to death of the previous person?

I have stage IV cancer and personally vastly prefer death to being frozen. I'm frankly baffled by those who think cryopreservation is a good idea given the threat that unaligned AGI poses.

[edit to add:] BTW, this isn't rationalization. I've felt this way about cryopreservation for many years before I knew I had cancer.

Bad feelings are vastly less important than saved lives.

Omega: Hey, supposedlyfun. You are going to die in a car crash tomorrow. Your child will grow up without you, your family will never get over it, and no aligned AGI will recreate your mind once technology allows it. But! I can prevent that death if you let me torture a random person for a year, inflicting on them the maximum possible amount of pain that their nervous system can experience, at every interval of Planck time during the year. But I will then give that person instant therapy that undoes all the damage. What say you?

supposedlyfun: No. 

*

How do you square your argument with my preference here? 

I appreciate that you went through the effort of sharing your thoughts, and as some commenters have noted, I also find the topic interesting. Still, you do not seem to have laid bare your assumptions that guide your models, and when examined it seems most of your musings seem to miss essential aspects of valence as experienced in our universe. I will be examining this question through the lens of total utilitarian consequentialism, where you sum the integral of valences of all lives over the lifespan of the universe. Do specify if you were using another framework. 

When you conclude "Bad feelings are vastly less important than saved lives.", it seems you imply that 
1) Over time our lives will always get better (or positive) 
2) That there's always enough time left in the universe to contribute more good than bad. 
(You could otherwise be implying that life is good in of itself, but that seems too wrong to discuss much, and I don't expect you would value someone suffering 100 years and then dying as better than someone dying straight away). 
In a S-risk scenario, most lives suffer until heath death, and keeping those lives alive is worse than not, so 1 is not always true. 2 also doesn't hold in scenarios where a life is tortured for half of the universe's lifespan (supposing positive valence is symmetrical to negative valence). It is only when considering there's always infinite time left that you could be so bold as to say keeping people alive through suffering is always worth it, but that's not the case of our universe. 

More fundamentally, you don't seem to be taking into account yet non existing people/lives into account, the limited nature of our universe in time and accessible space, or the fungibility of accumulated valence. Suppose A lives 100 years happy, dies, and then B lives 100 years happy, it seems there's as much experienced positive valence in the universe as having had A around happy for 200 years. You call it a great shame that someone should die, but once they're dead they are not contributing negative valence, and there is space for new lives that contribute positive valence. Thus, it seems that if someone was fated to suffer a 100 years, it would be better they die now, and that someone else is born and lives 100 years happy, than trying to keep that original life around and making them live 200 years happy after the fact to compensate. Why should we care that the positive valence is experienced by a specific life and not another ?
In our world, there are negative things associated with death, such as age related ill heath (generally with negative valence associated), and negative feelings from knowing someone has died (because it changes our habits, we lose something we liked), so it would cause less suffering if we solved ageing and death. But there is no specific factor in the utility function marking death as bad. 

With these explanations of the total utility point of view, do you agree that a large amount of suffering (for example over half the lifespan of the universe) IS worse than death? 

This is basically Christian theology with permadeath being the state of hell (which is often referred to as the death of the soul) i.e. irreversible loss of value. At the same time it is believed that any amont of suffering in the current reality will be reversed and eternally compensated in heaven.

If there are no such states then all damage is probably not reversible, and lives have a maximum range in time of about 150 years. If suffering allows for more lives, which are equally suffering, and there is nothing to sustain the claim that it will be reduced in someone, then maintaining these lives is pointless. (In the christian view, there is a transcendent guarantee, that if certain condition are met in conscious choices, then any amount of experienced suffering will be compensated. In an atheistic worldview, there isn't necessarily such a guarantee for all scenarios.)

It should also be noted that suffering probably limits your ability to save lives. So these hypothetical scenarios are never directly causal, and thus mostly unlikely.

I think this post is extremely interesting, and on a very important topic. As I said elsethread, for this reason, I don't think it should be in negative karma territory (and have strong-upvoted to try to counterbalance that).

On the object level, while there's a frame of mind I can get into where I can see how this looks plausible to someone, I'm inclined to think that this post is more of a reductio of some set of unstated assumptions that lead to its conclusion, rather than a compelling argument for that conclusion. I don't have the time right now to think about what exactly those unstated assumptions are or where they go wrong, but I think that would be important. When I get some more time, if I remember, I may come back and think some more about this.

If one must choose between a permanent loss of human life and some temporary discomfort, it doesn't make sense to prefer the permanent loss of life, regardless of the intensity of the discomfort. 

This choice doesn't exist; permanent death is inevitable under known physics. All lifespans are finite because the time the universe will support consciousness is most likely finite, whether because of heat death or the big rip. This finiteness makes your "you save one life, and 7 billion humans suffer for 100 billion years" question not at all obvious. Saving a life is not avoiding death; it is postponing it. Thus, you could rewrite your scenario as: "should I give someone 80 extra years of normal life before they die, if in exchange, instead of dying at their normal time, 7 billion humans are tortured for 100 billion years and then die." Under a Rawlsian veil of ignorance, I would not choose to "save the life" in this scenario. Even if that person survived until the end of the black hole farming era, I probably still wouldn't choose it. There is too much chance that I will end up being one of the tortured. (Though a ${10}^{-10}$ chance of ${10}^{68}$ years of life against ${10}^{11}$ years of torture is pretty tempting on an expected value basis, so I'm not sure.)

As others have commented, I also think the reversibility of suffering is a weak point. We do not know how hard it is. It may have the same difficulty level as resurrection. But, if you specify that the finite span of torture happens instead of normal death, you avoid this.