I use both Kroil and Flitz.
I believe Flitz is a German invention. I use it in the bore too.
I'm working on a 20 gauge that had some bad rust after sitting in an unheated cabin past 2 years.
Here's a couple of pics before and after using Flitz only on the portion where the two big spots of rust were.
I do use Flitz on my shotgun rib too with a q-tip.
It's not magic but another option for you. Flitz is found in most gun shops.
It will not hurt bluing.