From memory this sounds very similar to a rifle at Horseshoe Bend National Military Park from when I was last there in the early 1980's. After getting to know the Ranger over several events, and under his direct supervision, was allowed to clean the crud and fouling off with damp cloth and tooth brush, removed the fouling from the bore with a brush and water, and remove the surface rust with Boeshield.
The bare piece of chert in the cock was replaced with a black English flint with leather cushion, the ferrous parts were lightly coated with Boeshield, and the stock lightly wiped with a cotton cloth with a small amount of Renaissance wax.
The rifle was kept in a transparent display case and only the Rangers were allowed access to it. It was generally not well cared for by gun enthusiast standards. I had photos, but they were lost in Katrina.
Regards,
Carl