What a nice find.
She seems to me to have the 4th type barrel and gas collar, which would make her a 3rd model American. Serial number range 20000-32800. Shipping dates for this series being May 1873 to Dec.1874. She may or may not have come from the factory with the lanyard ring installed. However it looks like a factory installed screw, as they went to be nickeled once complete. Guns of this butt style did have the serial number off centred forward on the butt as your example shows.