Well it ain't yer fault it was rusted. Sounds like some numb-nut popped some caps and then stuck it in the garage, or worse yet put it away after firing without cleaning, or not cleaning well...but, whatever. We won't whup you with the knotted plow line...this time!
Yeah, I would Navel jelly it, then steel wool the whole thing and then cold blue it with Super-Blue.
When I use super blue, I put it in a big bowl, the whole container, and dilute it a bit with water, (24%?) then put a rag about wash-cloth size in it. Then I hang the barrel, from a wire or string, muzzle down, and with the rag good and sopping with the blue, apply it to the barrel. Just start slopping it on from the breech down. Keep doing it over and over...slop slop slop.
You'll get a good even blue. Actually you'll get a nice blue/black, which is actually more "PC" than a blue.
Obviously you want to do this outside or in the garage, where the excess bluing can slop and drip on the floor. It's messy but will give you a real even coverage. Barrel does not need to be hot, but should at least be warm.
Now the cold blue/black is not real durable, and will fade to a grey/black, with handling and use, which I really like. I think it looks great. But I'm the guy that also "ages" my brass. Some people would prefer it to stay shiney and new looking, and polish their brass, but I really like the aged, "patina" or faded look. At any rate it won't stay shiney bright blue-black for long. Again I like the look as it fades to grey-black, and it becomes non-reflective as it does this.
Another option is to lightly steel wool it with very fine steel wool and oil after it's blued, and you will get a nice artificial grey "patina"
[url] look...in[/url] other words it will look like a barrel that was originally left in the white, and went grey after years of use. I did that to my 1861 and it came out really nice. When I got my '61 it looked like a chrome rifle, and there just wasn't time to let it naturally age before I took it hunting...and I wasn't going to try hunting with a chrome rifle!!! I mean, it was certainly beutiful...but.....
Good luck. Not to worry.
Rat