Rembrandt, I think you have the basics down pretty well.
Hand lapping is a skill process and I would not undertake it promiscuously on the typical factory rifle. (What did you buy, anyhow?)
I fell for the Tubb Final Finsh version of fire lapping and shot gritty bullets through two barrels. I had broken in a factory barrel very laborously and it did not do much for it. It coppered and did not shoot as accurately as the Internet Experts said it should. The Final Finish procedure smoothed the factory barrel and made it easier to clean and also advanced the throat measurably. It did not make it more accurate.
I replaced the factory barrel with a name brand "hand lapped" job. I did not fire lap it but went through the manufacturer's 40 shot break-in which gradually reduced its tendency to copper... which was not nearly as bad as the factory barrel to start with.
The other was a good quality name brand hand lapped barrel. I had put it through the maker's 13 shot break in when new but had it rethroated for a different bullet just before I got into the Tubb system. So I just shot the finer grits in accordance with Tubb's recommendation. It did not affect that barrel any way I can tell, cleaning, accuracy, or throat length.
I have some Final Finish bullets that I may use to try to smooth up an old and somewhat eroded barrel, but I doubt I would put them through a new barrel again.
As far as the break in rituals, I figure I would follow the maker's recommendation. If I had a McMillan barrel, I would not break it in; otherwise, do as the maker says. None I have seen ran to a hundred rounds, and the late stages of the 40 round session above was good for load development and zero so it was not a waste of barrel life; that shooting would have had to been done anyhow.
