I don’t normally come here but……
We have got ourselves in a mighty tis was, and it might be worth reading Hardening and Heat Treatment more carefully.
Basically there are two separate processes.
There is the the slow carburisation process, which involves old bits of bone, leather etc, and more “modernly” various carburising powders. The process involves (normally) sealing in some airtight box, (not always depends on the powder)raising all to the appropriate temperature and then iron being a solid solution, the carbon migrates through the material at a particular rate enriching the surface with carbon before being quenched. It is slow, but depth of case can be more or less as deep as you want, properties are very controllable and there is les risk of distortion. Much used in industry.
The other is the Kasenit type process, much more suited to our sort of setup and effective enough for what we want.
Nothing inferior about anything, nothing went wrong – just a case of the right powder for the wrong process or vice versa. Full details are in Tubal Cains book in the chapter about case hardening.
Brinne is a good idea if you are stopping a tempering/heat treatment process (at say light straw), or if distortion is likely to be a problem – mostly it isn’t because the substrate is in our cases mostly non heat treatable mild steel. We don’t really toughen or otherwise heat treat solid steels other than Silver steel.
It has little effect on case hardening because all one is doing is freezing the crystal structure in the martensitic condition. IOW you are stopping the carbon rich surface from transforming back into pearlite, which it will do if allowed to cool naturally. So as long as you cool it faster than it can transform, and that you will do with water, the system will work perfectly.