The measurement of the ball being 16mm seems to be incorrect. You say the diameter of the bullet-casing's "tube" is about 13mm, and your first group of photos show the ball is smaller than the opening in the "tube."
A precision-measuring Digital Caliper, like the one in the photo below, can be bought online from Harbor Freight Tools (or on Ebay, or at Home Depot stores) for about $15. It's well worth that price, because super-precise measuring is ery important for correctly identifying other relics, such as belt-buckles, coins, and buttons.
I'm going to wait for precise measurement of the bullet-casing before I say anything else about it.