I have a 788 with a Timney and a custom Jury 1-12 barrel debating method of barrel break in if any.
Don't bother.
Just shoot it until the groups start to open up, then clean back to the bare steel with a good copper/carbon solvent and start developing a load.
Kenney Jarrett was once asked how he came up with his "barrel break in procedure" He now wishes he'd never come up with one, but only did so because customers kept asking him to.
Same with the moa out of the box guarantee with a specified load, proprietary to that particular rifle/cartridge combo. It's only come back to haunt him.
IMHO, it is quite possible to shoot a barrel to the point, accuracy drops off and it's impossible to bring it back. Many match shooters of all venues have had this happen.
I had one barrel ruined by cupro nickel jackets, because the jacket compound welded itself to the steel in such a manner that when it was removed, it took bits of the rifling edges with it.
I believe, as others do, the composition of the bullet jacket material, along with the intensity of the loads, has more to do with initial accuracy than any other issues.
Most loaders I know try to wring out every bit of velocity for bullet weight they possibly can. Sometimes bypassing the best accuracy nodes in favor of speed.
Shoot ten to twenty cartridges with a starting load, see how well they group. That will give you a very good idea whether the rifle will shoot well or not.
Use your normal procedure for working up a load, considering what the rile will be used for. Hunting rifles don't need to be accurate for ten to twenty shots or more in a string. Shooting such strings only tells you what the rifle will do when the barrel is hot.
When you're hunting in the field, other than for Gophers, if you didn't bring the animal down with the first two shots, very likely you aren't going to harvest that animal. Those first two shots from a COLD barrel are the most important. Yes, it's nice to be able to say your rifle will deliver tack driving accuracy for the first 5 or 10 shots, but under 99.9% of field circumstances the chances of getting that many shots off at an animal are a pipe dream, and quite realistically, most rifles aren't manufactured with that kind of shooting in mind.