The situation described in The Egg replaces morality with a direct reason not to harm others, because you are the person who will suffer because of it. So if you're complaining that the story's premise kinda eliminates our usual ideas about morality, my response is: Yes. That's part of what makes it an interesting story.
As for the meta-time thing, functional decision theory [1] solves this. The application is particularly clean because your memories are erased between lives. There's no factor of 2 free lunch from temporal ordering.