First: New bronze bore brush used dry (no solvents), working slowly and methodically for a dozen or more passes to allow the bronze bristles to cut through the accumulated leading. Bronze is much harder than lead, but much softer than the steels used in your revolver, so this cannot cause any harm in any way.
Then: Normal cleaning with solvent and patches.
Next: Assuming residual leading that the new bronze bore brush will not remove, try an old worn bore brush wrapped with strands of 0000-grade steel wool, another dozen or so passes through the bore. Again, steel wool is much harder than lead but much softer than the steel used in your revolver, no harm at all.
Follow with the usual solvent and patch cleaning exercises.
Note that I have specified 0000-grade steel wool, the finest grade you will find. You can rub the blued finish of your vintage S&W revolvers all day long without damage to the bluing.
Learned this method at the post armory at Fort Benning, Georgia, on a working detail cleaning US and foreign weapons heavily used in training, including Commie-bloc steel-jacketed bullets fired on full-auto all day long. Worked 50 years ago in harsh examples, works just as well today with a little bit of accumulated leading.