Leave the bbl and cylinder chambers open. They don't get any rust bluing soln applied to them so you won't be doing any carding to those surfaces.

Wipe out the bore and chambers with a clean patch after going thru the boiling water tank is about all I've ever done. The heat of the metal will make sure it dries from there.

Don't apply anything to the bore or chambers, just leave them bare metal. They won't rust or pit during the process as long as you don't put the parts through any extended rusting cycles like a couple days each..

The only time I ever protect the bores is when I do a damascus finish and that's only because betw the rusting cycles, the bbl has to go thru a dunking into an etching soln.
I have to keep that soln from getting at the surface of the bores. So I coat the bores of the bbl's with nothing more than shellac. A couple heavy coats with a swab on a cleaning rod and let dry.
It holds up very well thru the boiling water of the process. I sometimes re-coat at about cycle#6 or 7 just to make sure, but I'm not sure it even needs it. I don't want to find out the hard way though!.
Removal of the coating is not that easy, but plenty of laq.thinner into the plugged bore than wiping it clear w/swabs of the same gets it done,,finally.
Tough stuff.