Gotta add my 2 cents! I've been a shooter for over 60 years and just recently found a new way to clean barrels I believe will end the "first shot out " problem. Y'all have hinted at it; shoot a couple fouling shots b4 serious grouping. However, this is a much better way!
I have gone to the "pull it" method of cleaning. I spray or pour an oil down the barrel and pull a bore snake through. That is all ! WOW! I remember benchrest shooters would clean their barrels completely and dry it thoroughly THEN shoot fouling shots! DUH! Next, a fine barrel maker said NEVER shoot a dry barrel. Add it up, benchresters and barrel maker say and do the same thing. So, it makes perfect sense. Something else to consider; as the bullet goes down the barrel it will fill the pores in the steel making it smoother and then maybe less bullet interference? Whatever happens is a good thing. No more "cold barrel" shots. I also won't pull the snake til after a lot of shots. I have NOT seen ANY degradation of accuracy neither. New barrels? Shoot 5, pull one. Shoot 5 , pull one. Repeat for 20 shots. Maybe once a year I will use a cleaning rod and brushes and patches. IF accuracy is degrading. Oh, and my rifles are shooting sub 1/2 MOA with this method.