I always remove the bbl from the action. It's just the possibility of any oil or grease that is inside on those threads weeping back out onto the freshly blued surfaces with every coating that's done.
I may happen,,,it may not.
It may not happen on the first few coats, but then give you a problem on that last final coating you decided to apply just 'cause everything was going so great.

Boiling water and it's 212F degree heated steel liquifys any oil/grease down in there and it'll leak out at the most inopportune moment to spoil an otherwise nice job it seems.

Yes I'd gotten away w/o doing it. But I'd also paid the price of polishing and redoing a job or two because I didn't.
So now it's just the way I do things and has been for a long time.
Witness mark the bbl and reinstall back to that mark. There should be enough draw up if the bbl was installed correctly in the first place.
If there isn't and the thing just turns off with little or no effort to begin with,,you've got to fix that problem before ever worrying about rebluing it.

Careful handling, perfect fitting bbl jaws of poured lead that are lined with one wrap of newsprint and a sprits of rosin make sure nothing is marked during reassembly.

A higher gloss is obtainable with most any soln with shorter rusting times, sometimes addingin slightly lower humidity and temps.
Easy on the carding wheel pressure, let the wheel do it's burnishing work.
But some soln's and steel combinations just naturally are more agressive than others and will etch very quickly.
It just takes experimentation and experience to get to know what's what and even then the work will show you a new trick or two just when you think you've got it all figured out.
You'll never get a high gloss if you don't polish to one either.

I don't plug them or coat the bores either for rust bluing.