Your Fort Laramie bridge, as shown in Bridgehunters, appears to be an improved Murphy-Whipple design, as compared to the 1859 Whipple Iron Bridges used on the Beale Wagon Road. Improvements seen in the 1875 Fort Laramie through truss bridge, built by King Iron Bridge Co., include: 1. rivets and 2. pin-connections of the segmented bowstring. Robert P. Murphy is said to have invented the pin-connection concept around 1860.
Not being a bridge engineer, I probably missed other improvements that one might have noted.
Thanks for noting "Custer's Bridge Too Far."