I Havea nice Remington 22-250 That I did it the old way I was tought.
1 shot clean
2 shots then clean
3 shots then clean
4 shots then clean
5 shots then clean
6 shots then clean
7 shots then clean
8 shots then clean
9 shots then clean
10 shots then clean
http://i10.photobucket.com/albums/a1.../22-250low.jpg
http://i10.photobucket.com/albums/a139/robster1776/items%20for%20sale/22-250thumbhole.jpg
I have never had any problems breaking a barrel in that way