Couple of thoughts. It has helped me to take a small file and open up the rear sight notch a bit. Then, for shooting groups, use a target that has a white or yellow bull surrounded by a black ring. For fifty yards the white needs to be about 6 in. in diameter, and 12 in. for 100 yards. With this setup you can more easily center the front sight, be it bead, blade, or inverted V in the rear notch and also in the target circle.
Another thought is to mount an aperture sight at the rear. This increases your sight radius and generally solves the problem of getting a sharp front sight picture. Not wanting to drill and tap, I have used JB Weld to bond Williams aperture sights to the receivers of Mausers and a Krag carbine. This is fairly easy to do. I realize some may not want to do this to a valuable collector piece, but mine are strictly shooters. They say you can remove a JB welded piece by heating, but I am leaving mine on because I want to shoot 'em and the peep sight is not obtrusive. If you use a target of the type described above, you will have an aperture in front of your eye and an aperture at the target plane, and your eye will do a great job of centering the front sight in both, for precision shooting.