Swank, IMO if the Frizzen is making a lot of sparks and the flint isn't being damaged, be happy.
I wouldn't think of trying to carburize and reharden a Frizzen that's working well. You might want to use a dry whetstone or a wet one with water to try to remove some of the cross frizzen marks tho. Don't use oil of any kind on the frizzen face.
Stone in the same direction that the flint will fall.
A good, properly hardened frizzen should last for many thousands of shots.
Fox:
The comment about the top cock screw hitting the Frizzen was made because I once saw a Flintlock which had too short of a flint installed. Because it was too short, it stood about 5/16 off of the frizzen face at the half cock position. During firing, as the cock fell, the screw hit the frizzen just after the flint did. This started to push the frizzen back which lifted it off of the flint resulting in no spark and no ignition.
Oh, speaking of oil on the frizzen face, you might try using acetone, alcohol or other degreasers on it before shooting.
A lot of people do oil their frizzen faces to prevent rust which is good, but oil can keep the flint from biting into the metal and cause it to skid if it is not removed before shooting.
As for flintlocks which work better when they have large spaces between the flint and frizzen at half cock, it sounds like just another quirk one must know about for that gun.
As with everything else about Black Powder Muzzleloaders, each one is different, almost like people.