Funny. My instincts are telling me that there's a Utility Monster behind that bush.
I'm not satisfied with the lifeist or the anti-deathist reasoning here as you present them, since both measure (i.e. life-count) and negadeaths as dominant terms in a utility equation lead pretty quickly to some pretty perverse conclusions. Nor do I give much credence to the boxed subject's own opinion; preference utilitarianism works well as a way of gauging consequences against each other, but it's a lousy measure of scalar utility.
Presuming that the box's inhabitant would lead a highly fun-theoretically positive fifteen minutes of life by any standards we choose to adopt, though, pressing the button seems to be neutral or positive (neutral with respect to my own causal universe, positive relative to the short-lived branch Omega's creating) -- with the proviso that Omega may be acting unethically by garbage-collecting the boxed subject when it has the power not to.
I would feed the utility monster.
(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.