uscra112
You are correct about the switch from muzzle loading to breech seating near the end of the schuetzen era. The big switch to breech seating coincided with the emergence of smokeless powders such as Schuetzen Smokeless, Bulk Shotgun and Sharpshooter plus better primers, giving equal accuracy to duplex or semi-smokeless powders. 
Muzzle loading made sense with duplex and semi-smokeless as most of the fouling was pushed through the barrel and out the open breech when ramming a bullet down the barrel. Breech seating with those powders required barrel cleaning between shots or powder fouling prevented seating subsequent bullets.
With smokeless powder, breech seating was easy shot after shot as powder fouling was minimal. This made the extra steps required for muzzle loading no longer necessary.
The attached photo shows bases of muzzle loaded and breech seated bullets. Both bullets were .001 over grooved diameter. Those fins protruding from the breech seated bullet must not be of any real consequence as that particular rifle is killer accurate.
To keep everything in proper historical perspective remember, schuetzen was an all offhand game.

Not being an aeronautics engineer, I can't see that the 'fins', if evenly arranged would hurt accuracy. Maybe long range trajectory, but not at our one and two hundred yards. Even revolver bullets that get the devil of a beating before leaving the barrel make it to the target very nicely.

I believe I read somewhere that loading with a false muzzle was to conserve energy and not get tired out during a long  match.  They stood the rifle in the racks that you see in so many pictures of old shooting shacks.  Kept them from lifting heavy rifles a lot. Bob

Randy 
The rifle that was used was a Pope the bullet came from the mold that Pope cut for that gun. All the Pope breech seating bullets that I have seen have what to my mind is an extreamly heavy base, but thats the way Pope cut them.

40 Rod

My 38-55 ML Hepburn rifle is most accurate when I can see a ring of light around the bullet when at the breech ready to fire. Groove diameter and over groove diameter bullets are not nearly as accurate. My assumption is that the the tight fitting bullets disturb or remove the bullet lube in the grooves. Had one target where the first seven shots were solid twenty fives. Eighth shot went low in the twenty two, ninth shot low twenty two. Messed around and found I had hard fouling just ahead of the chamber. Seating a bullet felt normal but was actually seating on the hard fouling. Cleaned the barrel and the last shot was a twenty five. Now I use a dedicated loading rod with an adjustable brass thingamabobber. If theingamabobber doesn't touch the false muzzle when loading I know something isn't right. 

         Joe.

Bore guide with a set screw is what it really is. Flip it over for a bore guide.

      Joe.

Necessity is the mother of invention. Also helps to be a tight wad.   

        Joe.

Schuetzenmeister
Shoot them enough and rifle barrels wear out. It's nothing new. Chris Westergaard wrote in the American Rifleman magazine back in the 1920's that he finally switched from muzzle loading to breech seating his schuezen rifle because a muzzle loaded bullet would no longer stay in place ahead of the chamber. That section of the barrel had worn so loose, a muzzle loaded bullet would drop into the chamber.