All heat treat advice here sounds good enough, but are you sure that soft frizzen faces are the problem? Do both locks behave about the same? Is one or the other heavily worn?
With respect, it is my opinion, and observation, that flint lock frizzens were made of solid wrought iron, with the steel face forge welded or brazed on. Brazing was, I think, used for the common commercial grade, forge welding for military or top notch sporting arms
Trying to deep-case wrought iron might give you a surprise, such as blisters raised up here & there.
The differences between wrought iron and 18th century English steels I can discuss on another thread if you wish.
Brazed frizzen steel on American lock with only modest use (I think)
Anyway some locks like flint bevel down, others bevel up. Friction, and lock geometry is important. My 10th grade geometry teacher left me with measles one summer, I am definitely not the expert here. There are a lot of smart flint lock guys on this forum, though
No good at geometry, but I am a metallurgist with some interest in history. Over the last half century I have observed that for almost all metal Widgits that don't work, "bad metal/heat treatment" is not often the problem.
There are lots of ways to screw up heat treating. Especially if you are new to the subject. Me, I'd spend a lot of time looking at the mechanics of the thing, before I put it in the fire.