There are as many "correct" break in procedures as there are people who have typed them out. They run all the way from cleaning after every shot for a couple hundred rounds, to none at all. You'll just have to pick one you think works. :t
The rules for breaking in a rimfire and a centerfire are completely different as you aren't working with nearly the same metals.
I think what you are looking for by Chief Dave is listed under the Stinger (Barrel) Test Results at the top of the page, 10/22 Stocks and Barrels forum page.
It shows how he broke in the Stinger Barrel and the groups got smaller as the break in progressed.
Hope this helps. Andy:t