Yes Mark Lees solution for hot rust blue works well. The older Belgian Blue solution works well too but can easily leave you with a matted finish as it's abit more aggressive. Plus the merc in it isn't something I want in the area. The 'new' stuff has it too I think from the way it plates out on a piece of hot brass, copper, or your nice gold inlays!
On larger parts like the barrels. let the water heat up the part instead of using a heat source like a torch. Uneven heating from a torch, will get the surface too hot especially in the tin spots and cause the solution to burn and sizzle. That will give you an etched patchy look. Lay on the solution with clean OOOO steel wool for the first couple of times helps even out the layers. If the part becomes too cold to almost immediately dry the solution as it's applied, put the part back in the tank and let it reheat. Add another coat right on top of the first without carding, but use the steel wool to apply. Work on the thinner parts first obviously. Rifle barrels can be coated, boiled, carded and recoated without needing to be reheated before that coating if you work fast enough. A fine steel brush wheel, not knotted up or twisted is needed. Do not press too hard in carding as even a very very fine wheel can start to produce a matted surface on the barrels as you're carding. You want it to brush the surface, not change the look of the polish under the blue. Brighter the polish and desired blue,,finer and less pressure on the wheel.
Some solutions just won't work with some barrel steels (especially newer modern steels) If you don't get blue black on the first coat (and everything else is right, temp, clean, correct water, etc). Try another solution at that point as extra coats won't cover a bad first one.