Used correctly, the Outers Foul-Out system will remove every trace of copper from the bore. It does NOT happen in one iteration however. Scrubbing and degreasing both the bore and the stainless rod may be required several times along with changing out the solvent.
I have had to hand lap one rifle barrel in the last 25 years. And that was a NOS 2-groove barrel I installed on a 1903-A3 Springfield (Remington). My borescope showed that barrel looked like it was rifled with a dull butter knife at the factory. It would actually shred a patch pushed though the bore.
Hand lapping saved that barrel, but that is not a job for the faint of heart. Extreme care must be employed - especially at the throat and muzzle to prevent belling. I would want to see exactly what it is in that bore before taking a lead lap to it myself. Is it built up copper, carbon, rough machining, or pitting?