A Krupp stamp by itself means little or nothing. There have been Damascus Lefever barrels that were stamped Krupp, even though we know Krupp never produced Damascus tubes. Most likely, some Damascus tubes were mistakenly stamped Krupp when they were still in the white and the Damascus pattern would have been difficult or impossible to see.
Steel is an alloy of iron, carbon, and other ingredients. The number of individual heats (batches), and recipies, and different processes to remove gasses and impurities that have been concocted since the advent of the steel industry make it virtually impossible to nail down the origin of a piece of Three Barrel Gun Co. barrel steel to a particular steel manufacturer over 100 years ago. Even with modern methods of production and modern spectroscopic analysis performed during melting, two consecutive heats calling for the same steel, produced in the same furnace on the same day by the same employees will have slightly different chemistry. It would be much more productive to try to find old invoices or billing records to determine who supplied unfinished tubes or barrel steel to a given gunmaker.