Actually this sounds worse than hell. In the traditional christian hell, you know that your life has meaning and purpose as one of god's creatures, so at least you have a transcendent reason for your suffering.
By contrast, the Atlantic article describes a nihilistic hell where your experience has no redeeming features whatsoever.
http://www.theatlantic.com/technology/archive/2015/05/immortal-but-damned-to-hell-on-earth/394160/
With such long periods of time in play (if we succeed), the improbable hellish scenarios which might befall us become increasingly probable.
With the probability of death never quite reaching 0, despite advanced science, death might yet be inevitable.
But the same applies also to a hellish life in the meanwhile. And the longer the life, the more likely the survivors will envy the dead. Is there any safety in this universe? What's the best we can do?