I have now received a "Letter of Authenticity" (AKA as "factory letter," "historical letter") from Roy Jinks, in which he describes this pistol as "a very interesting single shot," and classifies it as a ".22 Single Shot Third Model, Transition Variation."
The letter says that the pistol shipped on February 11, 1910, to William Hoegee Co., Los Angeles (which was a big mail-order sporting goods firm).
Here is the letter (the first page is the standard 3rd Model letter -- the interesting comments about this pistol are on page 2):