polishing barrel, brown haze doesnt go away

i've been trying to "polish" a neglected muzzle loader barrel but i cant get rid of the rust brown haze on the outside.
been using several grades of steel wool and when i look straight onto the barrel it looks nice and shiny silver, but when i look along the barrel there's still a rust brown haze.
does anyone know how to get rid of that?
i'm not a fan of using vinegar like is suggested on some websites and videos, i just end up with more rust or blackened parts that look worse than with the brown "patina" that was on there before.

@entropy: thanks for the tip on using muriatic acid, i'll give that a careful try. i'm always a bit careful with "patina" since 99% of what they call that is just plain old rust that was covered with some oil and keeps eating away at the metal.

@BBBBil: i think they only started using browning from the brown bess and later models.
this one used to be "in the white" when they were produced. i've seen several of them in a museum. when new back in the year 17hundredsomething they were polished which made them look like they had a nickle finish, to make them rust less. i asked the museum curator and he said they cover them with renaissance wax to prevent rusting while on display.

i couldnt get muriatic acid where i live but i was recommended a phosporic acid rust remover for surface rust by the local hardware store owner.
he told me to degrease the barrel, then spray on the phosporic acid and let it sit for a few minutes, then brush it with a hard brush.
worked like a dream, all rust that was inside the tiny pits on the surface is gone and the barrel now is a matt silver which doesnt look bad at all.
tomorrow i will give it a light polish with fine steel wool and then use the renaissance wax to seal the surface.