John, We don't know if this method has ever occurred to you or not, but with your extensive body of experience with thousands of different pieces of ordnance, you may have already tried a "hands-on" approach. Mike and I have found, in our travels around the United States, that, with a little practice you can ID the metal in most seacoast tubes and especially carriage and chassis parts by feel. Of course the item must be unpainted, but many that we look at, we find in that condition.
Using your innate sense of touch, you can get a surprisingly accurate and unique, tactile response from each of the metals you mentioned. As you rub your index finger lightly across cast iron, you sense that it feels rough even though the surface may be perfectly smooth. Thousands of pores, large and small make cast iron feel this way. Diametrically opposite is wrought iron. Not only is it extremely reluctant to rust, it always feels smooth. If you have ever felt a burnished surface, that is what wrought iron feels like. Steel lies half way between these first two as far as tactile response is concerned and can best be characterized by consistency of feel VS the ever changing feel of wrought iron or cast iron as far as friction goes.
Of course visual classification is notably accurate as well. A uniform rusting indicates steel, a distinct pitting pattern denotes cast iron and the rust in low spots only (wood grain effect) denotes wrought iron.
Mike and I rate visual discernment at 70% and tactile at 85% accuracy. So, unless you are doing a real scientific study, you can "Know" with some certainty, easily and without expensive equipment.
Mike and Tracy