(Apologies to RSS users: apparently there's no draft button, but only "publish" and "publish-and-go-back-to-the-edit-screen", misleadingly labeled.)
You have a button. If you press it, a happy, fulfilled person will be created in a sealed box, and then be painlessly garbage-collected fifteen minutes later. If asked, they would say that they're glad to have existed in spite of their mortality. Because they're sealed in a box, they will leave behind no bereaved friends or family. In short, this takes place in Magic Thought Experiment Land where externalities don't exist. Your choice is between creating a fifteen-minute-long happy life or not.
Do you push the button?
I suspect Eliezer would not, because it would increase the death-count of the universe by one. I would, because it would increase the life-count of the universe by fifteen minutes.
Actually, that's an oversimplification of my position. I actually believe that the important part of any algorithm is its output, additional copies matter not at all, the net utility of the existence of a group of entities-whose-existence-constitutes-utility is equal to the maximum of the individual utilities, and the (terminal) utility of the existence of a particular computation is bounded below at zero. I would submit a large number of copies of myself to slavery and/or torture to gain moderate benefits to my primary copy.
(What happens to the last copy of me, of course, does affect the question of "what computation occurs or not". I would subject N out of N+1 copies of myself to torture, but not N out of N. Also, I would hesitate to torture copies of other people, on the grounds that there's a conflict of interest and I can't trust myself to reason honestly. I might feel differently after I'd been using my own fork-slaves for a while.)
So the real value of pushing the button would be my warm fuzzies, which breaks the no-externalities assumption, so I'm indifferent.
But nevertheless, even knowing about the heat death of the universe, knowing that anyone born must inevitably die, I do not consider it immoral to create a person, even if we assume all else equal.
There is an interesting question here: What does it mean to say that I'm glad to have been born? Or rather, what does it mean to say that I prefer to have been born?
The alternative scenario in which I was never born is strictly counterfactual. I can only have a revealed preference for having been born if I use a timeless/updateless decision theory. In order to determine my preference you'd need to perform an experiment like the following:
Without thinking about such an experiment, it's not clear what my preference is. More significantly, when 30% of American adolescents in 1930 wish they had never been born, it is not clear exactly what they mean.
Now if you know I'm an altruist, then the problem is simpler: I prefer to have been born insofar as I prefer any arbitrary person to have been born, and this preference can be detected with the thought experiment described in the OP.
... unless I'm a preference utilitarian, in which case I prefer an arbitrary person to have been born only if they prefer to have been born.
How about: Given the chance, would you rather die a natural death, or relive all your life experiences first?