The new cat is fitting in pretty well.
Honeynut is tolerating him better now. I wouldn't call them "friends", but they're at least not bitter enemies. She tries to avoid him instead of fighting or hissing at him.
I've made a special effort to give Honeynut the same amount of love and attention that I give the new cat, so she won't feel neglected.
Weird thing: The new cat does not like kitty treats!