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 little clips that Yaelle posted look like a good idea; it seems like you just iron them on.