I spent three full days at the Buffalo Bill Historical Center with the Remington Society annual seminar in 2003 and again at the Buffalo Bill Center of the West with them in 2014. Those sliding out cabinets with the Bill Furnish collection and other guns is a grand improvement over the way they were racked in cases in 2003!! We did find that many of Bill's Remington doubles were mis-identified. Hopefully they have corrected that by now.
The .410-bore CHE-Grade Parker in a cabinet with "another .410-bore" is the Robert W. Woodruff gun --
The count I made in 2014 showed over 100 Parkers on display in the Cody Firearms Museum.