Dying quickly seems like it would really put a damper on the expected utility of being a copy.

Not if the copy doesn't anticipate dying. Perhaps all the copies go thru a brief dim-witted phase of warm happiness (and the original expects this), in which all they can think is "yup warm and happy, just like I expected", followed by some copies dying and others recovering full intellect and living. Any of those copies is someone I'd "like to be" in the better-than-nothing sense. Is the caveat "like to be" a stronger sense?

I'm confused - if agents don't value their past self, in what sense do they agree or disagree with what the past-self was valuing? In any case, please reverse the order of the Methuselah valuing of time-slices.

Edit: Let me elaborate a story to motivate my some-copies-dying posit. I want to show that I'm not just "gaming the system," as you were concerned to avoid using your caveat.

I'm in one spaceship of a fleet of fast unarmed robotic spaceships. As I feared but planned for, an enemy fleet shows up. This spaceship will be destroyed, but I can make copies of myself in one to all of the many other ships. Each copy will spend 10 warm-and-fuzzy dim-witted minutes reviving from their construction. The space battle will last 5 minutes. The spaceship at the farthest remove from the enemy has about a 10% chance of survival. The next-farthest has a 9 point something percent chance - and so on. The enemy uses an indeterministic algorithm to chase/target ships, so these probabilities are almost independent. If I copy to all the ships in the fleet, I have a very high probability of survival. But the maximum average expected utility is gotten by copying to just one ship.