Not an experiment as such, but some info to share. When I bought my Orion Barrel underhammer it had a nice brown, not very dark, but looking like it had been browned in its past. After I took it home I was talking to the seller and he told me it had never been blued, but sat in a cabinet in his shop for about 40 years. On the bottom flat you can see where someone head used a Magic Marker and wrote the twist and caliber. Otherwise, you'd think it was an amateur attempt to brown it.
My point is even if someone in the 1780's kept his barrel in the white, a few generations left in a closet etc would produce a brown barrel.
Just my thoughts.