For a queen size duvet I just stuff the entire duvet inside the cover and then align the two corners farthest from the hole, pinch from the outside and shake, takes less than a minute if I'm in a rush and no inversion required. I do have very long arms though, and maybe this would be faster for a king size duvet cover.
This is what I do as well basically. It's usually more confusing to me to figure out what's top and bottom versus sides than to actually put the cover on.
