Hi Tim,
In your case, it might be tough to harden and temper the flintcock (it is called a flintcock not a hammer). I routinely case harden the cock, frizzen and lock plate but I am set up with a heat treating oven and all the things I need. Hardening and tempering any part on a Chambers lock will also void his warranty. To solve your loose flintcock fit on the tumbler, using a small cold chisel, hammer creases on the back side of the cock around the square hole such that the the metal is pushed inward reducing the size of the hole. When you install it on the tumbler it should then be nice and tight and will stay that way.
dave