The main reason that the replacement barrels shoot better is that they have what's called a Bentz chamber, which is sort of a compromise between the long sporter chambers on factory barrels and target chambers on bolt action target rifles. They are made so that the bearing surface of the bullet just kisses the rifling. One disadvantage is that some ammo in some barrels can't be ejected without firing. Also, in many cases, the first shot, which is of course chambered by hand, will be out of the group of shots chambered by the firing cycle.
I had been using Eley subsonic hollow points in my squirrel gun, which has a Volquartsen carbon fiber tension barrel. They grouped the best, but the first shot was typically 1/2" or more out, usually high and right, and the chambered round can't be ejected by hand. My procedure was, load the chamber, fire a round into the ground, go hunting. On the way out of the woods, take out the magazine, fire the chambered round into the ground.
I tried a couple of other brands last week, and it looks like the SK subsonic HP is going to be the ammo of choice this year. It shoots nearly as well as the Eley, without the problems. It ejects, and the first shot is closer to the group.
This is 50 yards on a day with a very light breeze.
I also tried RWS, also a subsonic hollow point. It shot pretty well too, but I couldn't eject unfired rounds.