The 100% copper Chore Boy on a used brush works, the best option is the Lewis Lead Remover kit from Brownell's.
All the older revolver and lead bullet auto guys had a Lewis tool.
It pulls the lead out with no risk.
The trick is to back off the nut on the rubber head for the first pass or two.
Another, slower method is to liberally apply Kroil in the bore and let soak a day or so, then brush it out.
The Kroil is such an effective penetrating fluid that it infiltrates under the leading and loosens it.
"Shooting the lead out" with jacketed bullets is something people do for years, then one day they suddenly have a ring or bulge in the barrel.
When fired down a leaded bore the jacketed bullet has to push the leading in front of it like the bow wave of a boat.
Just a little more leading then usual and the leading can't be pushed fast enough and pressures soar. Result is something has to give and you get a ringed or bulged barrel.
In addition, some of the lead gets ironed onto the bore in a thin plating of lead.
This is difficult to see and sometimes the first sign of trouble is when a bit flakes off, exposing a pit in the bore.
To clean leading from chambers, Bronze chamber brushes from Brownell's are best.
These are not just larger diameter, they're made of a stiffer bristle then a bore brush.
Usually one pass through a chamber will remove all leading and fouling.
Don't use stainless steel brushes, they can ruin a chamber.