This has been discussed in several other areas of the S&W Forum site.
In at least 2 of those places, the ultimate lead removing technique was agreed; wrap a layer of 100% copper kitchen pot scrubbing material around the brass brush and scrub 20X through bore.
It won't ever harm steel, it's dirt cheap and locally available in your supermarket, Rite-Aid drug store, etc. Sells under names like Scotch Brite or Chore Girl or some such. Two dollars will buy you several years' worth.
Cut it with scissors and wind it around the brass brush.
I used to swear by a chemically impregnated cloth which I placed over a jag and pounded through the bore... twisted lead slivers clattered out the end and that was usually the end of it. But occasionally even that didn't work... when it didn't, the copper covered brass brush DID.
Lewis Lead Removers are still around here and there... in my area they show up most often in the BP section of gun shops. Relative to Chore Girl copper scouring pads, Lewis products are expensive.

This is attacking the symptoms, not the problem, of course. The problem is usually soft lead, high velocity and/or poor lubing of cast bullets... though a rough bore can contribute, too.

g'luck