Any advantage to cryo-treat brass instead of annealing? Has it been done?

I have no idea, but if cryoing the entire piece of brass does for the head, what annealing does for the neck, then you will be killed when you fire it.
I suspect it is more voodoo nonsense like cryo treating barrels was.

I'm with voodoo, that explains my experience with cryo BS!!

Brass, being a Copper Alloy, hardens only by working such as re-sizing a case or some other mechanical working; it only softens with heat.
Unlike ferrous alloys, you can't achieve anything but frustration from quenching; removes the heat, but doesn't change the temper of the material.

That said, cryogenic temp application to brass is, at best, an interesting experiment. More likely, as has been said, just more voodoo.