I've hand lapped crowns for high power rifles and saw a magazine article years ago by a fellow doing a revolver muzzle using a round-head bolt as the lap. He got excellent accuracy improvement, but I don't recommend the bolt because the head is ellipsoid, and if you don't keep it on the bore axis, it won't cut symmetrically. Like Mr. Hunter, I use a lathe anytime I have a barrel off a gun anyway, and with the 1911 that doesn’t take a lot of effort to arrange. But with a screw-in barrel, this lapping approach avoids disassembly and it isn't subject to chatter, as some piloted hand cutters are.
JB Bore Compound will not be adequate. It cuts far too slowly. You will want silicone carbide lapping compound. Valve lapping compound from an automotive supply place will work. Try to find a store that sells two grades rather than one, and get the finer of the two. Otherwise, buy 240 grit compound. You can polish as the final step using JB compound with the same lap tool. You want to polish because the silicone carbide will leave a rough texture that will rust easily if you don’t polish it.
The ball bearing is my preferred lap because it is hard enough not to change radius significantly during the process. Choose a ball which will produces a crown angle you want (see formula in my illustration). You will have to settle for the nearest available size. Get a half-inch brass tube from the hobby shop, scuff the ball on one side with 100-120 grit wet/dry sandpaper and glue the handle to the ball with JB Weld. Then take a Dremel tool and an abrasive cutoff wheel and put some grooves in the lapping face it to retain the lapping compound supply since, unlike brass, none will embed and stay in place on a chrome-steel ball.
You need a tuft of cotton pushed a quarter inch or so below the muzzle to catch loose grit. This is replaced whenever you change grit grades. The ball tends to be self-centering
if you start with the muzzle square, or are cutting through small damage or finishing a good original crown, since it will tend to re-center once damage or flaws are cleared out. If the muzzle is out of square, the ball will walk away from the tall side, which creates a useless crown in that bullets will be tipped by the resulting uneven exit jetting of propellant gases against their bases as they exit the muzzle.
So, if your muzzle is out of square, or your original crown is off-center, you either need to invest in a 90° cutter to clean the end to square it or square it by other means. With the 1911, having cylindrical sides at the muzzle, you can file the old crown off and use a machinist’s square to check and correct it for squareness. M.L.McPherson has been known to do this at the range, after cutting a barrel to get it to a vibratory sweet spot. He commented that he gets weird looks, applying hacksaw and files to his gun barrel. It takes a bit of skill. And you will want to file a chamfer on the outside edge of a 90° muzzle so it doesn’t cut you accidentally when you handle it.
The basic lapping procedure is the same regardless of what you are starting with. Check any assembled gun to be sure it isn’t loaded. Open the action to be sure this condition can’t change. Square the barrel if needed. Put the cotton in. Apply compound to the lap. Hold the barrel muzzle-up between your knees. Place the lap against the muzzle and its tubing handle between your palms. Spin it back and forth 5-10 times by rubbing your palms back and forth against the handle. Rotate the barrel about a third of a turn and repeat. Rotate another third and repeat. Periodically take a Q-tip and wipe the compound off the crown and inspect it to check your progress. You will be done for shooting purposes when you have an even grayish lapped surface texture from the inside of the lands to the bottoms of the grooves, and a small uniform ring of marking just outside the grooves. If you are starting from a 90° muzzle, this happens quickly; usually in just the first three turns of the barrel. However, you will likely want to go further to recess the crown a safe distance to protect it from bump damage.
The back and forth motion plus the barrel rotation randomizes the lapping action so it doesn't favor one side or the other. This is done lapping valves in an engine as well. Technically, you should be rotate the start point of the ball handle 1/3 turn, as well as the barrel, but I don't find I grasp it in exactly the same spot after rotating the barrel, nor do I rotate it back and forth the exact same amount each stroke, so it tends to get randomized on its own. Avoid the temptation to chuck the lap in a drill. Unidirectional motion tends to cause the lapping compound to squeeze away from some contact points and clump and scratch harder at others, leaving streaks and tool marks on the crown surface. Go with randomization. It doen't take much time. This is a 15 minute job if you don't add what I describe in the last paragraph (in which case it takes a half hour to forty minutes).
When you have cut deeply enough, pull the cotton out with plastic tweezers (to avoid crown edge damage) or moisten it with a few drops of oil and push it out from behind with a cleaning rod. Then use Bore Scrubber or another spray cleaner to remove all traces of abrasive from the bore and crown and from the lap and from the cleaning rod, if you used one. Plastic tweezers would be dissolved by this spray, but we don't care what they have on them anyway. You just need to decontaminate abrasive from the rubbing items so you may change abrasive particle size or avoid turning your cleaning rod into an abrasive lap. Now you are ready to repeat with the JB Bore Compound (not to be confused with the JB Weld, please).
If you own a series of different grades of lapping compounds, you can work your way down through them, finishing with a bit of white diamond substitute buffing stick or Dico stainless steel grade buffing stick rubbed into the lap. Assuming your compounds stepped down in size to 1200 grit, this will result in a mirror surface with absolutely no tool marks. It is the prettiest crown you’ve ever seen, bar none.
Nick