The duvet cover thing was really cool but it looks like you would be unable to connect the corners of the duvet to the inside corners of the duvet cover. You want to have them snapped or clipped or tied so that you can sleep without worrying about bunching inside and being left with open spaces of empty cover.
The way I’ve always done it, the way the Swiss do it, is almost as easy. Lay the duvet out on your bed or floor. Turn the cover inside out. Tie the two corners away from the duvet cover hole to two corresponding corners of the duvet. Then stick your hands into the (still inside out) duvet cover and grab the already tied corners and shake the whole thing down over the duvet. Tie the other two corners inside the cover, near the hole. Then button the cover up. Done. It’s not that much harder and your duvet is secure in place for the most tossing and turning nights.
Here is one way to snap them together. There are others.
https://www.amazon.com/Corner-Keepers-Comforter-Shifting-Install/dp/B00RMVIHL4/ref=sr_1_6?s=home-garden&ie=UTF8&qid=1480491173&sr=1-6&keywords=duvet+cover+clips
I once tried that inside out method trying to follow the video and I was doing something wrong - couldn’t make it work for me.
I may try your method - I have just been pushing the duvet inside the cover and grabbing the corners, pulling them down inside, and then getting the corners on the upper portion and shaking it. I have three beds here with duvets so I have to do this a lot.
Those are great, but years ago I just said forget about it & our down comforter goes commando now. Put a quilt on top to keep it clean & it feels warmer & softer against your skin. I’ll never go back to a cover.