I decided to “cone” the muzzle of my White Mountain Carbine, to ease loading. Pacific Tool and Gauge made a piloted reamer for me.
Imagine a ball entering the muzzle from left to right, in the drawing above. It is pressed into about a 0.530" muzzle, gently tapering to 0.513" (just a little over groove diameter). Then there is a sharper 20 degree transition to my 0.501" bore.
This was an interesting project. The patched ball is now held securely as it awaits a short starter, and accuracy did not suffer.