Well, when you state that “personhood itself is unnatural in the animal kingdom”, it’s obvious where you are coming from. Nevertheless, that assumption is patently false (and pretty anthropocentric ;). You should really check chimps, gorillas, and other animals (e.g. elephants) that exhibit self-awareness, culture inheritance, etc. You’ll be in for a great surprise.
As for morality, I can only guess how you came to the conclusion that it “is about making the real world conform to ideals”, because to me it always meant either a set of rules of a particular community (no matter how right or wrong they are) or the most rational responses that lead to “goodness”, which I have, for a long time, associated with a state of emotional and intellectual peace or equilibrium. A sort of psychosomatic homeostasis. Lo and behold, today I checked the Stanford Encyclopedia of Philosophy, and it seems to be the common descriptive and normative definition of morality (sans the definition of “goodness”).
Anyway, when I say that “moral choices are natural”, I mean exactly that — nature is not amoral. The five universal don’ts I mentioned (don’t kill, don’t steal, don’t cheat, don’t lie, don’t covet) lead to the homeostasis I mentioned above. But again, if you thrive on conflict, anxiety, disgust, fear, etc. you will definitely see it in a different way.
And just as a side note, if you have a keen eye, you will notice that those moral “laws” seem to work even among animals.