One thing that had been bugging me on the Mac is that when I would create a new contact from Apple Mail, that contact would go into the group, “On My Mac.” I had been trying to move exclusively to iCloud to sync my address book across my Mac, iPhone and iPad. The solution is extremely simple and I am a little embarrassed I never found it before. In the Address Book settings, it is possible to choose your default account.
I set this and now newly-created accounts go directly into iCloud. No need to open up the Address Book and move the contact between groups.