Not meant to be left in the bore.
Iosso works well but it needs to be wiped out right after cleaning and the bore oiled.
Iosso is an abrasive paste and should be treated as such. The black residue you picked up wasn't oxidation, which stainless does do, only invisibly.
I went through a similar bout with Iosso when I was shooting competitively. Didn't matter how much you cleaned, the patches came out dark until the bore was wiped clean and an oily patch was run through the bore.
Iosso will clean the bore right down to the bare metal, of everything including carbon residue and jacket fouling. Not great for lead fouling.
I just stick to Wipe Out now.