I actually don't think any of those things are problematic. A reductionist view of personal identity mainly feels like an ontology shift - you need to redefine all the terms in your utility function (or other decision-making system), but most outcomes will actually be the same (with the advantage that some decisions that were previously confusing should now be clear). Specifically:

Does the reductionist view of personal identity affect how we should ethically evaluate death?

I don't think so! You can redefine death as a particular (optionally animal-shaped) optimization process ceasing operation, which is not reliant on personal identity. (Throw in a more explicit reference to lack of continuity if you care about physical continuity.) The only side-effect of the reductionist view, I feel, is that it makes out preferences feel more arbitrary, but I think that's something you have to accept either way in the end.

For instance, if continuing to exist is like bringing new conscious selves into existence (by omission of not killing oneself), and if we consider continued existence ethically valuable, wouldn't this imply classical total utilitarianism, the view that we try to fill the universe with happy moments?

Not really. You can focus your utility function on one particular optimization process and its potential future execution, which may be appropriate given that the utility function defines the preference over outcomes of that optimization process.

Also, the idea of "living as long as possible" appears odd under this view, like an arbitrary grouping of certain future conscious moments one just happens to care about (for evolutionary reasons having nothing to do with "making the world a better place").

This is true enough. If you have strong preferences for the world outside of yourself (general "you"), you can argue that continuing the operation of the optimization process with these preferences increases the probability of the world more closely matching these preferences. If you care mostly about yourself, you have to bite the bullet and admit that that's very arbitrary. But since preferences are generally arbitrary, I don't see this as a problem.

Finally, in the comments someone remarked that he still has an aversion to creating repetitive conscious moments, but wouldn't the reductionist view on personal identity also undermine that? For *whom" would repetition be a problem?

This basically comes down to the fact that just because you believe that there's no continuity of personal identity, you don't have to go catatonic (or epileptic). You can still have preferences over what to do, because why not? The optimization process that is your body and brain continues to obey the laws of physics and optimize, even though the concept of "personal identity" doesn't mean much. (I'm really having a lot of trouble writing the preceding sentence in a clear and persuasive way, although I don't think that means it's incorrect.)

And in case someone thinks that I over-rely on the term "optimization process" and the comment would collapse if it's tabooed, I'm pretty sure that's not the case! The notion should be emergent as a pattern that allows more efficient modelling of the world (e.g. it's easier to consider a human's actions than the interaction of all particles that make up a human), and the comment should be robust to a reformulation along these lines.