Heavybarrel...if Butch's Bore Shine is what you have used in other rifles for years and you haven't had any problems it is because those rifles don't copper foul. This will probably make a few people mad, but...that is probably one of the poorest performing bore cleaners available today. It ranks right up there with most of the "foaming" bore cleaners that also accomplish zero {unless you leave them in the bore for a week} and even then many still do nothing to copper.
The people that swear by Butch's almost invariably DO NOT own a borescope. If they did they would get over their infatuation with the stuff.
I have been lucky with the two 243's that I own, both are tack drivers, but I do know and have seen many 243 rifles that were picky about ammo, whether it be the powder and charge, the brand bullet or the seating depth.
Buy a new barrel if you want to, but I would definitely suggest getting some JB Bore Cleaner or Iosso paste and following the instructions first. What ever it says to do, do it twice. Good luck and good shooting.