Before I became anxious from watching that video I had a scope on a 270 Win, Mauser action, with clearance between the end bell and barrel would tolerate a single sheet of printer paper but not two. It was that way for over 30 years.
Would I do it again. Nah.....
A thought just popped into the ol' knoggin. Place a piece of scotch tape, about .002 thick on the barrel under the front edge of the end bell, put some chalk or some thing that will leave a mark on its top. Load and shoot then look. Heck, I'm full of dumb ideas like that