I use Lock-Tite Navel Jelly from hardware store. It is a gel form of phosphoric acid. It will take off the remaining bluing and can also give you that dark gray patina you are looking for.
It is lightly etching the surface of the barrel but not enough to feel. Still keep the gel out of the inside.
I usually hang the barrel with the nose down. Then brush on a coat of gel and keep it moist on the barrel with fresh coats for a day. I have accidentally let a coat dry before, but just used another fresh coat over the dried gel and that will re-moisten the dried on stuff.
Remove the gel with a damp rag. You can do more treatments until the patina is darker gray.
I did this GPR several years ago. It has continued to darken with age.
When fresh built:
[attachment=0:12ickn9k][/attachment]IMG_0176.JPG[/attachment:12ickn9k]
and now:
[attachment=1:12ickn9k][/attachment]GPR.jpg[/attachment:12ickn9k]