I believe accuracy could be improved by machining a couple of grooves in the insert to hold rubber O-Rings that would be a press fit in the chamber. That would take up all the manufacturing tolerance mis-match, and prevent the shakes & wobbles in the chamber.
Even a wrap or two of vinyl electrical tape might make them fit well enough to not rattle.
I have owned and used the long inserts with attached o rings and auto extractors and they are better, but they require grease on the o rings everytime they are removed from the chamber and in his situation he would have to remove the insert every shot.
True - but take a relook at that video and that is what you see - it IS off center.
If the video is showing a rimfire insert it will have to be bored off center in order for the centerfire firing pin to light off the rounds on a rimfire case.