Mr. Dale H. Eckerman Jr contacted me about the locomotive and offered this interesting background on the route and the engine: "By the way, the rail line (New Mexico & Arizona Railroad, owned by the Santa Fe RR and later by the Southen Pacific RR) through Elgin connected with mainline track in the East at Fairbank, Az, and in the West at Calabasas, Az). Therefore, it was certainly possible to get the engine and cars to the point of filming. Incidentally, there is more detail on the engine that was filmed - the way it was specially painted for the movie and how it was preserved after the filming. This engine (Southern Pacific #1673) is now on display at the Southern Arizona Transportation Museum in Tucson."
Following Mr. Eckerman's lead, a further search revealed this from The Tucson Weekly March 15, 2001: "The small community of Elgin was to play a major role in the history of the locomotive a few years later. In 1954, Hollywood decided to film the musical Oklahoma in the area and needed a way to get supplies and equipment to the site, a job the railroad could help with. Shooting began on the $6 million production in July and a cast and crew of 280 along with 100 extras was assembled. But the film needed an operating steam engine in one scene, so Locomotive #1673 served that function also, after being gussied up to look more authentic by adding a decorative smoke stack and a wooden cowcatcher. While actors sang about everything being up to date in Kansas City, a steam-spewing #1673 sat at the fictitious depot of Claremore in Oklahoma."