What is being overlooked here is the crosshead that existed prior to the development of the Alligator or Laird. In my many moves, I managed to lose my copy of Alfred W. Bruce's "The Steam Locomotive in America- Its Development in the Twentieth Century" - a must have for anyone interested in the subject, written near the end of of their long career.
Despite the subtitle, Bruce goes back to the earliest days of steam, with text and diagrams showing how each major component of the locomotive developed into its modern form. Look at the General, of 1854. Its crosshead was a four-bar design, neither Alligator nor Laird. In cross section, it was a square with each corner notched with a two-sided cut, looking like a fat cross with stubby arms.
If I had my Bruce, I could tell you when the Alligator or Laird types were introduced (and probably where and by whom - Bruce was comprehensive).
Glancing through my Prince ACL book, the four-bar type was widely used until the mid 1890s, which means most Americans and many early Ten-Wheelers, Moguls, Consolidations, and 0-4-0's had them. I see Laird-type (top guides) and Alligators appear in the 1880s, but not start becoming dominant until the mid-1890s.
Look at any American on display in a museum, and you'll see what I mean.
