A commercial product that I've used with great results is Shooter's Choice Lead Remover. Used as directed it takes care of light-to moderate lead deposits in pretty short order. Much faster than most of the "general use" solvent products that I've tried.
Another option for heavier stuff is Kroil. Given time to do its stuff, it'll get under the worst of it and loosen it to where a brush will peel it out.
A mechanical gadget that I've used with good result is the old Lewis Lead Remover. Don't know whether it's still in production, but Hoppe's makes an essentially identical item. It's caliber-specific, and takes more time and effort than the Shooter's Choice solvent on light-to-moderate stuff, but will save time on really heavy deposits.
One caveat on the lead remover cloths of whatever make: be extremely careful of where you rub them on blued finishes. They will damage or remove it. FWIW, I confine my own use of them to SS, where they're first-rate for cleaning the depositis and burn marks from the cylinder face.
The only experiences where I've gotten what I would consider even moderate leading with factory .38 Spl. loads were all with swaged 158 gr. HP "+P" cartridges. This was back when reliable JHPs were almost non-existent in any caliber and revolvers were still riding in virtually every LEO's holster. IIRC, it took a lot more than a box of them to get any of my weapons to that point. Most of the crud came from powder and lube fouling.
Without actually examining your weapon, it's pretty much impossible to tell whether there might be some mechanical issue contributing to the problem. There are a lot of theoretical possibilities, most related to tolerances in the bore, cylinder throats, forcing cone and/or the finishing thereof. If an examination by a knowledgable 'smith reveals a "rough" finish or over/under sized condition in the bore, throats or forcing cone, Taurus has a lifetime warranty and a reputation for honoring it.
