Why cut your pillow tick? Take a yard of it next time, and wash it, then line dry it. That removes all the sizing so your lube will stick better to the cloth. Then count off five stripes and tear off a strip 36" long.

I lay that over the muzzle, set the ball on it, and short starter it under the muzzle. THEN I cut the strip of cloth away from the barrel. Now I have a perfectly centered patch.