Here are some photos of one of the armory reamers that I use. They do tend to be tough on the arm so I ream a couple of passes, the do another job for a while, and then back for some more passes, you get the idea. Sort of like rifling, it takes about 6 hours for the 700 or so cuts required. That six hours may take me a week!
This reamer will fit into a 0.43 minimum bore barrel and I use it up to about 0.56 cal. It is water quench steel, square in cross section with two corners sharp and two corners dull. It is fully hard with the exception of the lantern chuck end which is stress relieved. I shape the tool and quench vertically in brine. Any resulting warpage is taken away by a flat sheet of abrasive paper on the top flat platten of my table saw. This will straighten out any warp.
I do drive it with a brace, although I guess a variable speed drill on slow would be OK also. I find that the square reamer cuts very aggressively in wrought iron. The lantern chuck is of brass. You can put a dab of epoxy to allow the tool to be pulled back if you wish.
The shim is hardwood and I use regular notebook paper for shims & plenty of oil. It is really interesting how aggressive a cut one of these square armory reamers will take. (The wood shim is made from a popsicle stick - but don't tell anybody). I think that I can ream a rough wrought iron barrel to a mirror finish in a couple of hours if I work straight through. The shim will butt up against the brass lantern so it stays in place. However I have found that this is not needed as the shim/paper will stay with the reamer and not slip off without the shoulder.
Also, I have found that modern reamers and drills are very difficult to keep on center in a barrel, they will tend to wander off and do a disappointing job. The 18th c armory reamer will certainly stay exactly on center as you smooth the bore.
Jim Everett