I watched my German friend Gerold Pheffer fit several barrel sets to guns( two of which were mine). He fit the barrels to the receiver without the hinge pin being installed. After he was satisfied with the fit, then he marked and cut the "hook" in the barrels. He polished with a fine cut file, loaded with chalk and oiled; that is removing almost no metal in the final fit. He "filed like a machine", at times working thousandths of an inch from thousands of dollars worth of engraving, without putting a scratch on it. Amazing. It may help if you remove the hinge pin, fit the barrels, then replace the pin.
Mike