Pathfinder,
Thanks for the detailed question. Yes, both ends of the rivets are countersunk, on the face plate side they are countersunk quite a bit, at least half the thickness of the plate. They do not seem to interfere at all with the flint action.
A comment about the casehardening and carburizing of frizzens. When we case harden using an 18th c method, only carbon is added to the metal surface. In this case hardening, or carburizing, the steel surface acts just like spring steel and can be stress relieved, annealed, hardened and tempered just like 1090 or 1075 steel. When we use a modern case hardening compound there is more than just carbon being added to the metal, I believe that much of modern case hardening compounds actually nitride the metal to increase hardness. Now this process acts differently than the traditional method and you may not be able to draw or temper the part.