Pretty much any such moral standard says that you must be better than him

Why does this need to be the case? I would posit that the only paradox here is that our intuitions find it hard to accept the idea of a serial killer being a good person, much less a better person than one need strive to be. This shouldn't be that surprising - really, it is just the claim that utilitarianism may not align well with our intuitions.

Now, you can totally make the argument that not aligning with our intuitions is a flaw of utilitarianism, and you would have a point. If your goal in a moral theory is a way of quantifying your intuitions about morality, then by all means use a different approach. On the other hand, if your goal is to reason about actions in terms of their cumulative impact on the world around you, then utilitarianism presents the best option, any you may just have to bite the bullet when it comes to your intuitions.