I had to refit the frizzen to priming pan fit on many of the Brown Bess locks for my old Military Reenacting Unit and that was for Pedersoli and Japanese/Miroku Besses. The India made guns had not come out yet. The reason was many of them were losing all or most of the priming pan charge when doing the "Cast About" as part of the Manual of Arms when loading and firing.
If I did not have to reharden the frizzen, as it seems you do not have to do, then it made it much easier and especially if the fit of the frizzen to pan was not grossly off.
I have been trained to file steel FLAT, by hand with a hand file. So the first thing I did was wrap some 120 Grit Emory Cloth around a flat file and gently go over the bottom flat of the frizzen just to make sure it was flat. For most of the frizzens, I did not have to take much metal off, but for some I did. After I got it flat, I went over it with emory cloth of 180, 220, and finally 340 grit to polish it. This mainly to help keep it from rusting as easily when lightly oiled.
Then I put a layer of Dykem Lay Out Dye on the top of the pan and that includes the top of the "support arms" (that is referred to as the pan bridle) ahead of the pan. Actually, there is no need for the bottom of the frizzen to contact the top of the support arms, so I filed them down a few thousandths lower than the top of the pan.
Then I put the frizzen screw through the frizzen, but no frizzen spring. I smacked the frizzen down with a soft mallet and when the frizzen is raised, the now bare spots showed the "high spots" that had to be filed down.
To file down the high spots on top of the pan, you can use diamond files or wrap emory cloth around a flat file and use that to file the hardened surface down. After a little sanding/filing, you need to re-coat the top of the pan with candle black, black magic marker or dykem and whack the frizzen down again to see how the fit is progressing. It is a file/sand and check progress until the frizzen fits down well on top of the pan. I guess I went a little overboard on the muskets I did, because I worked the fit until almost no light showed between the parts.
Oh, I don't believe it is necessary to reharden the top of the priming pan or even the bottom of the frizzen when doing such work, unless you have to take a LOT off the bottom of the frizzen. When I say "a LOT" I mean 10 thousandths or more off the bottom of the frizzen and I never found that necessary.
Oh, I just had an idea. Do you happen to have a feeler gauge set that is commonly used to test the gap on spark plugs? If so, it would probably be a good idea to use it to check the gap at the back of the pan and inform us how much gap there is back there when the frizzen is closed down as it now stands.
Gus