Fouling is a function of how hard the sides of the bullet press outward against the bore. The force from that, multiplied by the friction coefficient is what is tearing at the copper. The Barnes are hard to push into the rifling and are springier, so their static outward pressure is higher to start, and they are fired at much higher pressures in high power rifles, and outward upsetting force from the high pressure adds to the outward upset. This is why copper fouling is usually highest just out in front of the throat, because that's where the bullet is when the pressure peaks.
Boretech Eliminator is an excellent general purpose bore cleaner. Way better and faster and less toxic than the ammonia-based copper removers. I keep it at the range in a little pump sprayer and at the end of a session squirt two or three pumps down into the chamber with the muzzle down. I watch to see it makes it to the muzzle. At that point, I have some silicone stoppers I push into the muzzle and the back of the chamber and I pack up and go home (about a 50-minute drive). Generally speaking, but the time I get hope, the bore is clean and just has to be patched out with a wet patch and a five-minute wait, followed by a dry patch to confirm no additional copper needs to come out.
Old or stubborn carbon is best tackled with Slip2000 Carbon Killer.
Extra heavy copper is most quickly removed with KG-12, though it has a cyanide compound it is and is more toxic than the Bore Tech product. It also doesn't produce any really obvious color change, so you may be happier with Bore Tech Cu++, which is more aggressive than Eliminator, but slower than KG-12.