I did some hot blueing back in the mid 60s. Found the only way I could quickly and harmlessly remove rust, down to the bottom of any pits, was to chemically dissolve it away with a short soak in a 1:1 mix of muratic acid and water. The acid is a concrete cleaner, Lowes has it by the gallon and one should be more than enough. (Mix by adding acid to the water, not the other way around.) The finished and cleaned results were easily hot blued with no later rust rising on the metal.
Use the acid outside, with plenty of ventalation and don't let the fumes reach any other ferrous metal or it WILL cause rust on them! Use it in a steel, glass or plastic container, NOT aluminum.
Degrease the metal as well as you can. Cover it completely with the acid mix and stir it a little maybe every ten minutes for a half hour or so. While longer soaks won't harm the steel it can etch the surface slightly, but not as much as blast cleaning would do. And blasting may not get to the bottom of the rust as the acid surely will!
When the visible rust has turned completely black, remove the action, flush it with running water a few minutes and then soak it a few more minutes in a solution of baking soda and water (actually, a carbonated soft drink will do!) to kill the remaining acid. Remove, dry and spay it with any light oil to prevent flash rusting of the super clean bare metal as you remove the residue.
Remove the black rust residue with a light wire brush on a grinding tool. When clean, re-oil it and store in a very dry place until it gets to the gunsmith who will finish the job.
Use rubber gardening gloves and cheap safety/eye goggles to keep the acid off you. Have a garden hose and a gallon or so of baking soda solution handy to immediately flush/kill any spills while you work with it. Dilute the acid bath with lots of water and pour it where it will not kill any grass or flowers; it's really not very harmful after it's diluted.
Understand that muratic acid is not terribly strong but it's usually limited to professonal use. Breathing the fumes can damage your lungs and burn the surface of your eyes so treat it with respect. But it WILL do what you want, completely, if you are a careful worker. If not, stay away from it!