The last thing I would use as a "cleaner" is a mixture of Aluminum Oxide and Kroil. Aluminum Oxide is an "Abrasive" we use to "Hone" cylinders and bores. All machinist know this, and use it, as an abrasive cutting compound, continued use of this WILL make your bore bright..........at the expense of making your bore bigger! FWIW
Sir, with all due respect you are incorrect. Aluminum oxide will not damage in any way shape or form your steel barrel.