Ok , I saw this post and have a bit of knowledge. Back almost 50 yrs ago, my father was friends with a famous trap shooter Larry Gravestock. Larry shot a single barrel pump (It was a Mod 31 Remington, I just looked it up) and the barrel was bent upward to such an extent that was obvious to anyone that looked at it. His technique was to put the barrel in a lathe between centers and crank the tailstock until it bent the barrel (cold) to where he wanted it. I think there was possible issue with the rib, coming apart, I saw him do this and the rib just bent with the rest of the barrel, but I was just a kid. Of course, there was testing and tweaking, but that is how he did it. His shooting style in trap was to spot shoot after calling for the bird and the extreme bend up of the barrel would take care of the rest. Crazy, but it worked for him. He actually made his money shooting live pigeons in very exclusive circles (usually in Europe), where wagers were astronomical over sometimes just a single bird, . A very clandestine side to the shooting sports.