Slide the sight out, peen the dovetail just a tad, and drive the sight back in. Get the thing where you want it and use a punch to stake it if needed. You will not need to peen the sides of that dovetail in much at all.
I have not done this on any Mosin, I have done this trick on several other rifles, mostly abused muzzle loaders over the years. Folks are always whanging muzzle loader sights left and right like it is some kind of contest.